# Thread: Derivative of definite integral?

1. ## Derivative of definite integral?

Is it possible to take the derivative of a definite integral? I guess if we have an indefinite one, like:
$\int f(x)\,dx$, taking its derivative, we would get $f(x)$, right?

What if we had $\int_a^b f(x)\,dx$?

2. wouldn't it be 0? because the solution to the indefinite integral would be a constant, derivative of a constant = 0.

3. Yes, that is correct. $\int_a^b f(x) dx$ is a constant and its derivative is 0.

4. Thanks guys.

seld, you meant definite integral right? (not indefinite).

5. Originally Posted by scorpion007
Thanks guys.

seld, you meant definite integral right? (not indefinite).
Yes, because indefinte integrals can be written as a function of x provided that one of the limits of integration is constant and the other is some x. But a definite integral is a number, and as hallsofivy said, the derivative of a number is always zero.

6. Originally Posted by scorpion007
Thanks guys.

seld, you meant definite integral right? (not indefinite).
er . . . yes, wow maybe I should stop posting after explaining analysis for about 2 hours to people . . . yes that's a typo thingy

7. Originally Posted by scorpion007
Is it possible to take the derivative of a definite integral? I guess if we have an indefinite one, like:
$\int f(x)\,dx$, taking its derivative, we would get $f(x)$, right?

What if we had $\int_a^b f(x)\,dx$?
$\int_a^b f(x)\,dx$ is a definite integral.
A definite integral is a number. What is the derivative of a number?