# Basic integration question

• September 9th 2009, 08:11 AM
N736RA
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!
• September 9th 2009, 08:24 AM
VonNemo19
Quote:

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

$\frac{d}{dx}\left[\frac{1}{3}\left(t^3|^{x^2}_{x}\right)\right]$ ?
• September 9th 2009, 08:32 AM
tutor.mathitutor
The attached document contains the answer.
• September 9th 2009, 08:33 AM
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?
• September 9th 2009, 08:35 AM
N736RA
mathitutor, thansk for that solution! That clears it up
• September 9th 2009, 08:43 AM
VonNemo19
Quote:

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

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