# Thread: Derivative of a Integral

1. ## Derivative of a Integral

If f(x) = $\int_1^x \sqrt{t^2+3}dt$ , then f(2)=?
The integral is from 1 to x^2 but I couldn't figure out how to do that in the integral. Everything else is right.
So the answer is 4 $\sqrt(19)$ but I got $\sqrt(7)$.

2. Originally Posted by IsaHanswille
If f(x) = $\int_1^x \sqrt{t^2+3}dt$ , then f(2)=?
The integral is from 1 to x^2 but I couldn't figure out how to do that in the integral. Everything else is right.
So the answer is 4 $\sqrt(19)$ but I got $\sqrt(7)$.
FTC ...

for a constant $a$ and $u$ a function of $x$ ...

if $f(x) = \int_a^u g(t) \, dt$ , then $f'(x) = g(u) \cdot \frac{du}{dx}$