Question

Find the area between the curves on the given interval. y = x3 – 1, y = 1 – x, -2 ≤ x ≤ 2

Answer 1

this is going to suck because you have to divide the region up in to several intervals

Answer 2

http://www.wolframalpha.com/input/?i=x^3-1%2C+x-1+domain+-2..2

Answer 3

wow okay

Answer 4

you can see that they switch places, so you are going to have to compute
\[\int_{-2}^{-1}(x-1)-(x^3-1)dx\]
\[\int_{-1}^0(x^3-1)-(x-1)dx\]
\[\int_0^1(x-1)-(x^3-1)dx\]
\[\int _1^2(x^3-1)-(x-1)dx\]

Answer 5

each of these is very easy, but doing 4 of them is a drag

Answer 6

so i will integrate them or?

Answer 7

yes, but of course simplify them first

Answer 8

each is either \(x^3-x\) or \(x-x^3\) depending

Answer 9

so the anti derivative will either be \(\frac{x^4}{4}-\frac{x^2}{2}\) or the other way around
it is easy, just a pain

Answer 10

ok

Answer 11

have fun

Answer 12

ok so i got -x^3 - 3/2

-x - 1/4

1/2 - x^3

and 15/4 - x