In three dimensions there are integrals for the volume and the surface area of a solid with a curved boundary. Integration can also be used to determine the mass of a body where the density of the matter inside it is allowed to vary from place to place. Integrals can be used to calculate the best aerodynamic shape for a spacecraft like the shuttle. The aerodynamic shape of the shuttle greatly affect the speed and maneuverability of the shuttle which helps in sending the shuttle into orbit. Once the shuttle takes off, there are people constantly calculating the integrals that will help to determine the best trajectory on the trip into space.
Integrals also play an important role in population growth calculations.
Medical scientists, insurance companies, biologists, and politicians are all interested in predicting the size of various populations, both animal and human, depending on their interests. The easiest approach assumes that the growth in size is always proportional to the current size. In reality, this is impossible because after a while there wouldn't be enough food, water, or space for the exponentially increasing number of individuals. So a more realistic model is built through the use of differential equations, perhaps by including a competing population, whether its rabbits or bacteria, with dynamics of its own. If a scientist is looking as some factor in particular, he can derive a differential equation and incorporate into it factors like a declining birth rate or an increased death rate.