## anonymous 5 years ago what is the area of the region bounded by the curves: y = x^{3} - x & y= 7x-x^{3}

1. anonymous

$curves: y = x^{3} - x and y = 7x - x^{3}$

2. anonymous

"I meant for there to be spaces between "and"

3. anonymous

Relatively easy - I just want to make sure I got the right answer: 16

4. anonymous

$2x^3 = 7x$ $\implies 2x^2 = 7$ $\implies x= \sqrt{7/2}$ So the area between the curves is $\int_0^{\sqrt{7/2}} [7-x^3 - x^3]dx = \int_0^{\sqrt{7/2}}[7-2x^3]dx$ $=7x - \frac{2x^4}{4} |_0^{\sqrt{7/2}}$

5. anonymous

I don't get 16.

6. anonymous

Oh whoops. I missed an x there.

7. anonymous

Should be $=\frac{7x^2}{2} - \frac{2x^4}{4} |_0^{\sqrt{7/2}}$

8. anonymous

But I still don't get 16