Question

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

Answer 1

\[curves: y = x^{3} - x
and
y = 7x - x^{3}\]

Answer 2

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

Answer 3

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

Answer 4

\[2x^3 = 7x\]
\[\implies 2x^2 = 7\]
\[\implies x= \sqrt{7/2}\]

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

Answer 5

I don't get 16.

Answer 6

Oh whoops. I missed an x there.

Answer 7

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

Answer 8

But I still don't get 16