Derivative of definite integral?

**scorpion007** · September 16th 2009, 09:04 PM

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 $\int_a^b f(x)\,dx$ ?

**seld** · September 16th 2009, 09:16 PM

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

**HallsofIvy** · September 17th 2009, 04:59 AM

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

**scorpion007** · September 18th 2009, 05:34 PM

Thanks guys.

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

**VonNemo19** · September 18th 2009, 05:43 PM

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.

**seld** · September 20th 2009, 10:32 AM

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

**Plato** · June 8th 2010, 01:24 PM

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?

Thread: Derivative of definite integral?

LinkBack

Thread Tools

Display

Derivative of definite integral?

Similar Math Help Forum Discussions

[SOLVED] Definite Integrals - Same Problem, 1st use Definite Integral, then FTC.

Finding a definite integral from other given definite integrals.

Derivative of a definite integral

finding the derivative of a definite integral

Derivative and Definite Integral question

Search Tags