# Integration - Fundamentals Thereom Of Calculus

1calculus1

## Homework Statement

$$\int_0^3\$$ (t-2)^1/3

## Homework Equations

Second of Fundamental Thereom of Calculus

## 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.

Homework Helper
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)

rootX
"(u^v)'=v*u^(v-1)*u'+u^v*log(u)*v'"

seems like a crazy expression

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

integrate (t-2)^2

Homework Helper
seems like a crazy expression

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

integrate (t-2)^2

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.

$$\int u^n du= \frac{1}{n+1} u^{n+1}+ C$$