# Thread: Basic integration question

1. ## Basic integration question

The solution to this problem is proving to be elusive, any insight would be appreciated!

The integral from x to x^2, with f(x) = t^2, and I'm looking for the derivative of that. Thanks!

2. Originally Posted by N736RA
The solution to this problem is proving to be elusive, any insight would be appreciated!

The integral from x to x^2, with f(x) = t^2, and I'm looking for the derivative of that. Thanks!
Would it not be

$\displaystyle \frac{d}{dx}\left[\frac{1}{3}\left(t^3|^{x^2}_{x}\right)\right]$ ?

3. The attached document contains the answer.

4. right thats what I thought it was, could you also write that as : (1/3)(x^5+x^3) ? or am I missing another step somewhere?

5. mathitutor, thansk for that solution! That clears it up

6. Originally Posted by N736RA
right thats what I thought it was, could you also write that as : (1/3)(x^5+x^3) ? or am I missing another step somewhere?
No... Watch

$\displaystyle \frac{d}{dx}\left[\frac{x^6-x^3}{3}\right]=\frac{d}{dx}(\frac{x^6}{3})-\frac{d}{dx}(\frac{x^3}{3})=6\cdot\frac{x^5}{3}-3\cdot\frac{x^2}{3}=2x^5-x^2$