# Differentiating an integral

1. Nov 15, 2007

### rootX

1. The problem statement, all variables and given/known data

$$\int_{x}^{2\,{x}^{2}+1}sin{t}^{2}dt$$

I need to take differential of that

2. Relevant equations

Fundamental theorem of calculus

3. The attempt at a solution

I know 't' is a dummy var, so I replace it with x,

and then
get
sin((2x^2+1)^2)-sin(x^2)

Can anyone please check my solution?

Thanks.

2. Nov 15, 2007

### Kreizhn

Look up Leibniz's Rule. After that it's just a plug and chug:

Edit: Leibniz Rule, not Theorem

Last edited: Nov 15, 2007