Definite Integration

Let  where f (x) is the integral of F(x).

As x changes from a to b, the value of the integral changes from f (a) to f (b). This can be shown as

Here, â€˜bâ€™ is called the upper limit and â€˜aâ€™ is called the lower limit of integration.

When integration is done within a defined limit, it is known as definite integration. In definite integration, we get a finite fixed value in the end, so there is no need to add the constant of integration.

Example
Solution

Properties of Definite Integrals

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•  if f (x) is an odd function

Note: A function f (x) is said to be an even function if f (â€“x) = f (x). A function f (x) is said to be an odd function if f(â€“x) = â€“ f (x).

For example: f (x) = x2 is an even function since (â€“x)2 = (x)2.

f (x) = x3 is an odd function since (â€“x)3 = â€“x3.

Example
Solution