|This article/section deals with mathematical concepts appropriate for a student in late high school or early university.|
A definite integral is an integral with upper and lower limits.
A definite integral is the area under the curve between two points on the function. In the picture below, the yellow area is "positive" and the blue area is "negative". The integral is evaluated by adding the positive area together and subtracting the negative area.
If the function f(x) is real rather than complex, then the definite integral is also known as a Riemann integral.
Solving Definite Integrals
Sometimes approximations, such as the Riemann Integral or Simpson's rule are used. These approximations are used when:
- The exact answer is not needed, only a close approximation. (Common in Engineering)
- The rule for integration is very complex. (Such as )
- The rule for integration is simply unknown. (Such as , the Zeta function)