ejaasaari/simplewiki-2025-04-01 huggingface dataset:
In calculus, an integral is the space under a graph of an equation (sometimes said as "the area under a curve"). An integral is the reverse of a derivative, and integral calculus is the opposite of differential calculus. A derivative is the steepness (or "slope"), as the rate of change, of a curve. The word "integral" can also be used as an adjective meaning "related to integers". The symbol for integration, in calculus, is: formula_1 as a tall letter "S". Integrals and derivatives are part of a branch of mathematics called calculus. The link between these two is very important, and is called the fundamental theorem of calculus. The theorem says that an integral can be reversed by a derivative, similar to how an addition can be reversed by a subtraction. Integration helps when trying to multiply units into a problem. For example, if a problem with rate, formula_2, needs an answer with just distance, one solution is to integrate with respect to time. This means multiplying in time to cancel the time in formula_3. This is done by adding small slices of the rate graph together. The slices are close to zero in width, but adding them together indefinitely makes them add up to a whole. This is called a Riemann sum. Adding these slices together gives the equation that the first equation is the derivative of. Integrals are like a way to add many tiny things together by hand. It is like summation, which is adding formula_4. The difference with integration is that we also have to add all the decimals and fractions in between. Another time integration is helpful is when finding the volume of a solid. It can add two-dimensional (without width) slices of the solid together indefinitely—until there is a width. This means the object now has three dimensions: the original two and a width. This gives the volume of the three-dimensional object described. Methods of Integration. Antiderivative. By the fundamental theorem of calculus, the integral is the antiderivative. If we take the function formula_5, for example, and anti-differentiate it, we can say that an integral of formula_5 is formula_7. We say "an" integral
Digimon (Kanji: デジモン, Hepburn: Dejimon) is a Japanese media franchise made by Bandai. It features a group of digital creatures called Digimon. Humans befriend Digimon as partners and work with them to protect both worlds from enemies. The series has movies, manga, anime, toys, video games, Digital Pets and card games.
Steven A. "Steve" Ballmer was the CEO of Microsoft Corporation from January 2000 to May 2014. He is the owner of the NBA team the Los Angeles Clippers after Donald Sterling was fired. He is the second person to become a billionaire in U.S. dollars based on being given shares in a company as an employee in which he was not the founder or related to a founder. In November 2023, "Bloomberg Billionaires Index" estimated his personal wealth at around $122 billion, making him the fifth-richest person in the world. In 2014 that he stepped down as Microsoft CEO. Family. His mother was an American Jew. His father was an immigrant from Switzerland who worked in Switzerland as a manager at Ford Motor Co in the late 1940s. In 1990, Ballmer married Connie Snyder. They have three children. Ballmer's grandparents lived in Pinsk, Belarus. Steve Ballmer was born March 24, 1956. He grew up in Farmington Hills, Michigan. In 1973, he graduated from Hull College, and now sits on its board of important people. In 1977, he graduated from Harvard University with a degree in mathematics and economics. While in college, Ballmer managed the Chess Team, worked on the Daily News newspaper as well as the Daily Star, and lived down the hall from Bill Gates. He then worked for two whole years as a helper of a product manager at Procter &amp; Gamble, where he shared an office with Jeffrey Immelt, who would later become CEO of General Electric. In 1980, he Joined Stanford Graduate School of Business but left the college to work at Microsoft. On October 4, 2007, Ballmer was given an honorary citizenship of Lausen, Switzerland. Microsoft career. Ballmer joined Microsoft on June 11, 1980., and was Microsoft's 24th worker, the first manager hired by Bill Gates. At first he was offered a pay of $50,000 as well as a bit of ownership of the company. When Microsoft was made into a company in 1981, Ballmer owned 8% of it.
Tears are clear liquid made by the body to clean and lubricate the eyes. There are three different types of tears that the body makes: You can produce tears when you cry.
27 is a year in the 1st century. It was a common year starting on Wednesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Piso and Frugi. Deaths. Jesus of Nazareth
Andrew Bonar Law (16 September 1858 – 30 October 1923), commonly called Bonar Law (), served as Prime Minister of the United Kingdom. Law was elected to Parliament in 1900 as a member of the Conservative Party. He became leader of the Party in 1911. He was Lloyd George's Chancellor of the Exchequer and Leader of the House of Commons while Lloyd George served as Prime Minister during World War I. Law became Prime Minister in October 1922. He found out he had throat cancer and resigned in May 1923. He died in October 1923.
39 is a year in the 1st century. It was a common year starting on Thursday of the Julian calendar. At the time, it was known as the Year of the Consulship of Augustus and Corbulo
The pulmonary artery is a blood vessel that connects the heart to the lungs. The pulmonary artery carries blood that does not have much oxygen. The blood from throughout the body is taken into the heart by the right atrium into the right ventricle. The blood is pumped into the pulmonary artery and into the lung capillaries. When the blood passes through the capillaries slowly to absorb the oxygen from the lungs. The oxygenated blood is taken through the pulmonary vein back into the heart through the left atrium and the left ventricle. It is then pumped throughout the body. Anatomy. The pulmonary artery is an extension of the pulmonary trunk (lat. truncus pulmonaris), extending from the right ventricle; it is located in front and to the left of all the vessels that flow in and out of the heart, and brings venous blood to the lungs (the only one of the human arteries, except for the umbilical arteries of the fetus). The initial lobe of the pulmonary artery goes up and back and somewhat covers the beginning of the aorta. Next, lying to the left of the ascending aorta and in front of the left atrium, the pulmonary artery lies at the level of the IV thoracic vertebra under the concavity of the aortic arch. Here the pulmonary trunk is divided into: Between the initial lobe of the left branch of the pulmonary artery and the concavity of the aortic arch is the connecting tissue cord - the arterial ligament (Latin ligamentum arteriosum). This is the remnant of the Botal duct (Latin ductus arteriosus (Botalli)), through which the fetus and blood entering the right ventricle are redirected from the pulmonary artery to the aorta: a small circle in the fetal stage of development does not function. In the future, the duct is obliterated (parallel overgrowth of the oval hole in the atrial septum).
An artery is a blood vessel that carries blood away from the heart to other parts of the body. Almost all arteries carry blood with a lot of oxygen in it. The only arteries that do not carry oxygen-rich blood are the pulmonary artery, and (in a fetus) the umbilical artery. Every artery has three layers. The outer layer is a thick covering made of stretchy tissue. The middle layer is made of muscle, so the artery can get wider or get smaller when the body needs it to. The inner lining is made of the same cells that line the heart. Arteries are deep under the skin. They do not have valves to prevent blood from flowing backwards. Instead, every time the heart beats, the arteries stretch out so the blood has room to go through. Once the walls have completely stretched out, the muscles in the arteries make them shrink back to their normal size. This pushes the blood through. Arteries split down into small vessels called "arterioles". Important arteries. The aorta. The aorta is the main artery in the human body. It starts in the left ventricle of the heart, which is full of blood that just picked up oxygen in the lungs. (This is called "oxygenated" blood - meaning it has a lot of oxygen in it.) The left ventricle pumps this oxygen-rich blood out through the aorta. The aorta brings this blood to every organ in the body. The aorta runs all the way from the heart to the bottom of the abdomen. Along the way, smaller arteries split off the aorta, like branches on a tree, to bring blood to different parts of the body. The aorta finally ends by splitting off into the two arteries that bring blood to the legs. Except for the pulmonary artery, every artery in the body is connected to the aorta. Some other important arteries include: The pulmonary artery. The pulmonary artery is the only artery in the adult body that: The body uses the oxygen carried in the other arteries to make energy. The blood in these arteries becomes "deoxygenated" - it does not have much oxygen left in it. This blood then travels through capillaries to get from
Jönköping is a city in Sweden. About 90,000 people live there. It is in southern Sweden near the lake Vättern. Jönköping was actually 3 towns that grew into one large town. The 3 towns were, "Jönköping (55.000)", "Huskvarna (22.000)" and "Norrahammar (9.000)". Jönköping is the 9th biggest city in Sweden.
Warwickshire (pronounced //, //, or //) is a county in central England. The county town is Warwick. The shape of the administrative area Warwickshire differs considerably from that of the historic county. Commonly used abbreviations for the county are Warks or Warwicks. Warwickshire is perhaps best known for being the birthplace of William Shakespeare from Stratford-upon-Avon. The county has also produced other literary figures such as George Eliot (from near Nuneaton), Rupert Brooke (from Rugby), and Michael Drayton from Hartshill. Geography. Warwickshire is bounded to the northwest by the West Midlands metropolitan county, and Staffordshire, by Leicestershire to the northeast, Northamptonshire to the east, Worcestershire to the west, Oxfordshire to the south, Gloucestershire to the southwest. The majority of Warwickshire's population live in the north and centre of the county. The market towns of northern and eastern Warwickshire were industrialised in the 19th century, and include Atherstone, Bedworth, Nuneaton, and Rugby. Major industries included coal mining, textiles, engineering, and cement production, but heavy industry is in decline. Of the northern and eastern towns, only Nuneaton and Rugby (as the birthplace of Rugby football) are well known outside of Warwickshire. The rich towns of central and western Warwickshire include Leamington Spa, Stratford-upon-Avon, Kenilworth, Alcester, and Warwick. They have light to medium industries, services, and tourism as major employers. The south of the county is largely rural and has little population, and includes a small area of the Cotswolds. The only town in the south of Warwickshire is Shipston-on-Stour. The highest point in the county, at 261 m (856 ft), is Ebrington Hill on the border with Gloucestershire, GR SP187426 at its southwest extremity. There are no cities in Warwickshire since both Coventry and Birmingham were incorporated into the West Midlands county in 1974. The largest towns in Warwickshire as of 2004 are: Nuneaton (pop.
The Doppler effect is a change in frequency and wavelength of a wave. It is caused by the change in distance between the thing creating the wave (causer) and whatever is measuring seeing or hearing the wave (watcher or observer). Another word for "causer" is "sender" or "source". Another word for "change in distance" is "speed" or "relative velocity".  A common example is sitting in a car while another car goes by the watcher. The watcher will hear a change in pitch, while the sender will not. For waves read all the waves that can send out or reflected by an object. And for reflection read change of direction of a wave.  Effects of changes in distance. If observer and creator of the wave get closer, the frequency is higher and the wavelength is shorter. If the distance between the observer and creator gets longer, the frequency is lower and the wavelength is longer. Light waves can also be read, examples are: An extreme example of the doppler effect is an aeroplane flying at a faster speed than the speed of sound and how the wall of sound is heard on the ground.
Monagas Sport Club is a club of football from Maturín, Venezuela. Current roster 2007. Goalkeepers  Defenders  Midfielders  Forwards  Source. liderendeportes.com
Vättern is the second biggest lake in Sweden. The lake's total surface area is about . The deepest known point is . The average depth of the lake is . Vättern is famous for the quality of its transparent water. Many of the people living in the area get their drinking water directly from Vättern. The lake water does not need to have many things done to it before it is used in nearby cities and towns. The water can be safely drunk from almost any point in the lake. It has been said that Vättern is the largest body of potable water in the world. Vättern is also noted for its fishing. Tourist sport fishermen and people on vacation are allowed to fish in the lake as long as they do not use nets.
Uppsala is a city in Sweden. It is the 4th biggest city in Sweden, and the center of the Church of Sweden. The city is home to the well-known student residential area of Flogsta. It is the largest student residence in the city. It is also known for the 'Flogsta scream'. At 10 pm every evening, students scream their frustrations from windows and balconies.
The Summer of Love is the name for the summer of 1967 in the United States, especially in the Haight-Ashbury district of San Francisco, California. Thousands of young people from all over the world went to San Francisco to help create a hippie counterculture. The Summer of Love made the rest of America much more aware of the hippie movement. The Human Be-In is often called the start of the Summer of Love, although it happened in January of that year. During the Summer of Love, as many as 100,000 young people from around the world travelled to San Francisco's Haight-Ashbury district, Berkeley, California, and other cities in the San Francisco area. Once there, they joined in a popular version of the hippie experience. The people who were a part of the Summer of Love are sometimes called "Flower Children". When these new Flower Children returned home at the end of summer, they brought their new clothing, ideas and behaviors to most major cities in the U.S., Canada, Britain, Western Europe, Australia and New Zealand.
Appenzell Innerrhoden is one of the twenty-six cantons of Switzerland. It is the smallest canton by population and the second smallest by area. It is one of the only direct democracies in the world. Districts. The 6 (districts) of Appenzell Innerrhoden are:
Staffordshire (abbreviated Staffs) is a county in the West Midlands region of England. The county town is Stafford. Part of the National Forest is there. It is next to the counties of Cheshire, Derbyshire, Leicestershire, Warwickshire, West Midlands, Worcestershire and Shropshire. The largest city in ceremonial Staffordshire is Stoke-on-Trent.
The Upper Cretaceous is the last geological epoch in the Cretaceous. It began 100.5 million years ago, and ended 66 million years ago. The Cretaceous is traditionally divided into Lower Cretaceous (early), and Upper Cretaceous (late), because of the different rocks. The rocks reflect the conditions in which they were formed. From lowest to highest, it is subdivided into the Cenomanian, Turonian, Coniacian, Santonian, Campanian, and Maastrichtian ages.  The Upper Cretaceous is the time of chalk. Chalk is composed of countless millions of calcareous (CaCO3) plates called coccoliths. They are so small they can only just be seen with a light microscope; details require an electron microscope. The plates are formed by single-celled planktonic algae called coccolithophores, and were laid down in the off-shore seas.  The only other rock found in chalk is the flint, which is siliceous (silica, SiO2). This derives from those algae and animals which have skeletons of silica. Undoubtedly, this marks periods when the climate was somewhat different. The Cretaceous was the last period when dinosaurs were the dominant land animals. "Triceratops", "Tyrannosaurus" and "Velociraptor" lived at this time. The huge "Mosasaurus" was the dominant marine predator. In the Cretaceous period, birds became more diverse. Flowering plants developed more, and became the dominant plants on land. The Upper Cretaceous ended with the K/T extinction event. Extinction events. The end of the Cretaceous period is marked by the huge extinction event which marked the end of the dinosaurs. However, many groups had already disappeared long before then. There was an earlier extinction event in the Upper Cretaceous at the CenomanianTuronian boundary, about 95 to 90 million years ago. All we know about it is that there was huge volcanic activity which led to changes in sea life. The event brought about the extinction of the pliosaurs, and most
The Thai language is the national and official language of Thailand. It is the first language of the Thai people, Thailand's main ethnic group. Thai is closely related to the Lao language. In fact, some dialects of Thai and Lao are mutually intelligible, meaning that speakers of one language can talk with and understand speakers of the other language without knowing the other's language. Sounds. Thai is a tone language, like Chinese. Writing System. The Thai alphabet has 44 consonants: The alphabet has Thai numbers:
The New England Patriots is an American football team in the National Football League or the NFL. They are in the American Football Conference or the AFC. Their starting quarterback is Mac Jones. Cody Kessler plays the second string quarterback. The Patriots play in Gillette Stadium on Foxborough, midway between Boston, Massachusetts and Providence, Rhode Island. In the 2007 season, the Patriots have won all 16 games and became the first team with 16 wins and no losses. They would win 2 more playoff games and enter the Super Bowl at 18-0. However, they did not complete a historic 19-0 season, because they lost to the Giants. The Giants scored 17 points when David Tyree made a helmet catch and the Patriots scored 14 points. The New England Patriots won the Super Bowl in 2001, 2003, 2004, 2014, 2016, and 2018. They play in Foxboro, Massachusetts. They lost to the New York Giants in Super Bowl XLVI on February 5, 2012 in a rematch of Super Bowl XLII which their perfect season got spoiled. This time, the Giants scored 21 points and the Patriots scored 17 points. The Patriots lost Super Bowl LII to the Philadelphia Eagles. Several records were set during Super Bowl LII, including most yards gained in any NFL game by both teams combined (1,151) and fewest punts from both teams in a Super Bowl (one) and was the second highest point total in Super Bowl history by one (74). Nick Foles of the Philadelphia Eagles was named Super Bowl MVP. The Patriots also won Super Bowl XLIX against the Seattle Seahawks when Russell Wilson threw an interception on the final play. The Patriots scored 28 points and the Seahawks scored 24 points. The Patriots were originally called the "Boston Patriots", and played in Fenway Park. Their name comes from the city of Boston's importance in the American Revolution. Players of note. Patriots All-Decade teams. 2000s. On March 16, 2010, the Patriots Hall of Fame group selected an all-decade team for the 2000s: Bold indicates
The Aspidogastrea (gr. "aspid" - shield, "gaster" - stomach/pouch) is a small group of flukes. There are about 80 species.  The group is a subclass of the Trematoda, and sister group to the Digenea. Species are between approximately one mm to several cm long. They are parasites of freshwater and marine molluscs and vertebrates (cartilaginous and bony fishes and turtles). Maturation may occur in the mollusc or vertebrate host.  None of the species has any economic importance, but the group is of very great interest to biologists because it has several characters which appear to be basal.
Theropods ('beast foot') are a group of bipedal saurischian dinosaurs. Although they were primarily carnivorous, a number of theropod groups evolved herbivory, omnivory and insectivory. Today, they are represented by 10,000 living species of birds, which evolved in the Upper Jurassic from small feathered coelurosaurian theropods. Among the features linking theropods to birds are bipedalism, the three-toed foot, a furcula (wishbone), air-filled bones, feathers and brooding of the eggs. Early theropods. Theropods first appear in the earliest part of the Upper Triassic about 230 million years ago. They were the sole large terrestrial carnivores from the Lower Jurassic until the close of the Cretaceous, about 66 million years ago. Some of the earliest and most primitive of the theropod dinosaurs were:
In mathematics, a ring is an algebraic structure consisting of a set R together with two binary operations: addition (+) and multiplication (•). These two operations must follow special rules to work together in a ring.  Mathematicians use the word "ring" this way because a mathematician named David Hilbert used the German word "Zahlring" to describe these structures. The integers, the rational numbers, the real numbers and the complex numbers are all famous examples of rings. There are other, more unusual examples of rings, however they all obey the special rules below. Rules. The operations are used to combine two elements to form a third element. There are a few rules the set and the operations must obey to qualify as a ring. These are called ring axioms: Special Kinds of Rings. Some rings have additional properties from those mentioned above, these rings get special names: Commutative Ring: If "x" • "y" = "y" • "x" holds for every "x" and "y" in the ring, then the ring is called a "commutative ring". Ring with Unity: If there is a multiplicative identity element, that is an element e such that for all elements a in R, the equation e • a = a • e = a holds, then the ring is called a ring with unity. This element is usually written as 1. Division Ring: If every element of the ring except 0 has a multiplicative inverse, that is for each a in R\{0}, there exists an element a-1 in R such that a • a-1 = 1, where 1 is the multiplicative identity element, then the ring is called a division ring. Integral Domain: In a ring, it may be possible to multiply two things which are not zero and get zero as a result. If this is impossible in a certain ring, then the ring is called an "integral domain". Field: A ring with all of the above properties is called a field.