Integral
From Simple English Wikipedia, the free encyclopedia
An integral helps to find out how much space is under a graph of something. Integrals undo derivatives. A derivative helps to find what the steepness is of a graph.
This is the symbol for integration:
Integrals and derivatives are part of a branch of mathematics called calculus.
Integration helps when trying to multiply units into a problem. For example, if a problem with rate () 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
). This is done by adding small slices of the rate graph together. The slices are close to zero in width, but adding them forever 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.
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 forever 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.