evaluate this indefinite integral:

Question

anonymous · Answer

$$\int\limits_{-1}^{5} \left| x-4x^2 \right|$$

anonymous · Answer

best figure out what your piecewise function really is before you start

anonymous · Answer

I tried splitting it up into two equations but got confused

anonymous · Answer

first you have to solve $x-4x^2>0$

anonymous · Answer

whoops, definite integral, my post said indefinite

anonymous · Answer

Yeah, so would I just say x>4x^2?

anonymous · Answer

oh no!

anonymous · Answer

$x-4x^2$ is a parabola that opens down 
it is 0 at $x=0$ and at $x=\frac{1}{4}$ so it is positive between the zeros, namely on $(0,\frac{1}{4})$ and negative everywhere else

anonymous · Answer

here is the picture with the solution http://www.wolframalpha.com/input/?i=x-4x^2%3E0

anonymous · Answer

so I should probably do the alternate one so that it's positive right?

anonymous · Answer

thefore you have to break the integral up in to 3 (!) pieces
$$\int_{-1}^0(4x^2-x)dx$$
$$\int_0^{\frac{1}{4}}(x-4x^2)dx$$
$$\int_{\frac{1}{4}}^5(4x^2-x)dx$$

anonymous · Answer

alright, I think I can do it from there, thanks!

anonymous · Answer

yw