Math Help - Integration

1. Integration

HI,
Integrate int sign 2x-(3-x)^4 dx
lower limit -2 higher limit 2

The - sign infront of the bracket, do I work it thru the bracket or work out the power of 4, foil it out, then put thru the negative sign??

Is this right 2x(x-3)^4 from the above????
thanks

2. Re: Integration

First multiply it out, then multiply by -1: $-a^4$ is not the same as $(-a)^4$

3. Re: Integration

Making sure I got this right to what you are saying foil it out correct??

Then work in the negative into that?

4. Re: Integration

Originally Posted by HallsofIvy
First multiply it out, then multiply by -1: $-a^4$ is not the same as $(-a)^4$
I might add that $(3 - x)^4$ is the same as $(x - 3)^4$, which might make things a bit easier.

5. Re: Integration

As TheChaz says, $\int_{-2}^2 x- (3- x)^4 dx= \int_{-2}^2 x- (x- 3)^4 dx$ and if you don't want to multiply that, let u= x- 3 so that du= dx and x= u+ 3. When x= -2, u= -5, and when x= 2, u= -1 so that would give
$\int_{-5}^{-1}u+ 3- u^4 du$