# Integration - Fundamentals Thereom Of Calculus

1. May 25, 2008

### 1calculus1

1. The problem statement, all variables and given/known data
$$\int_0^3\$$ (t-2)^1/3

2. Relevant equations

Second of Fundamental Thereom of Calculus

3. The attempt at a solution

I don't know what to do first because I'm not used to questions with square roots. Once someone help me with the beginning, I can probably do it because after that it's all the same process anyways.

2. May 25, 2008

### lurflurf

use the power rule
(u^v)'=v*u^(v-1)*u'+u^v*log(u)*v'
or since v'=0
(u^v)'=v*u^(v-1)*u' (when v'=0)
in particular
[(t-2)^(4/3)]'=(4/3)(t-2)^(1/3)

3. May 25, 2008

### rootX

seems like a crazy expression

OP,
Square roots work exactly the same way.
Try simple example first:

integrate (t-2)^2

4. May 26, 2008

### Dick

May be crazy but it is true. Still I think rootX is just suggesting you try the u substitution u=(t-2) and then use the power law formula for integrals.

5. May 26, 2008

### HallsofIvy

Staff Emeritus
By the way- there is NO square root in this problem!

May be just me, but please do not use "square root" for all roots! It leads to things like people saying "3 squareroot of x" when they mean "cuberoot of x" and then it's time for the old two by four to come out!

In any case, a "root" is just a power- use the power rule:

Yes, make the substitution x- a= u and then
$$\int u^n du= \frac{1}{n+1} u^{n+1}+ C$$