Integral itu apa sih? Jelaskan dalam bahasa sunda ya

This article deals with the concept of an integral in mathematical calculus. For other meanings of "integral" see integration.

Dina kalkulus, fungsi integral mangrupa generalisasi area, massa, volume, sum, sarta total.  Teu siga di prosés differentiation, aya sababaraha harti nu béda ngeunaan integral, gumantung kana béda téhnikna.  Sanajan kitu, dua cara nu béda dina fungsi integrasi bakal méré hasil nu sarua lamun duanana digawekeun.

Integral kontinyu, fungsi nilai-riil positip f tina variable riil x antara sisi kénca a sarta sisi katuhu b nembongkeun batas wewengkeun ku garis x=a, x=b, sumbu-x, sarta kurva dihartikeun ku grapik f.  Leuwih resmi, lamun anggap S={(x,y):a≤x≤b,0≤y≤f(x)}, mangka integral f antara a jeung b mangrupa measure S.

Leibniz ngawanohkeun notasi baku long s keur integral.  Integral dina paragrap samemegna bisa ditulis .  Tanda ∫ ngalambakeun integral, a jeung b mangrupa titik tungtung interval, f(x) nyaéta fungsi nu di-integralkeun, sarta dx notasi keur variabel integrasi.  Sajarahna, dx ngagambarkeun wilangan nu takhingga, sarta s panjang singkatan keur "jumlah".  Sanajan kitu, téori integral modérn diwangun ku dasar nu béda sarta simbol tradisional ngan sakadar notation.

As an example, if f is the constant function f(x)=3, then the integral of f between 0 and 10 is the aréa of the rectangle bounded by the lines x=0, x=10, y=0, and y=3.  The aréa is 10c, so the value of the integral is 30.

Integrals can be taken over regions other than intervals.  In general, the integral over a set E of a function f is written ∫Ef(x)dx.  Here x need not be a réal number, but, for instance, a vector in R3.  Fubini's theorem shows that such integrals can be rewritten as an iterated integral.  In other words, the integral can be calculated by integrating one coordinate at a time.

If a function has an integral, it is said to be integrable.

The function for which the integral is calculated is called the integrand.

Integrals are sometimes called definite integrals to emphasize that they result in a number, not another function.  This is to distinguish them from indefinite integrals, which are another name for an antiderivative.

If the domain of the function is the real numbers, and if the region of integration is an interval, then

the greatest lower bound of the interval is called the lower limit of integration, and the least upper bound is called the upper limit of integration.