Question

Find the volume of the region enclosed by z=1-y^2 and z=y^2-1 for 0<=x<=54

I got : int (8-8y^2)dy

Answer 1

I got : int (8-8y^2)dy eval from 0 to 54 but it's wrong

Answer 2

Give me a second :P

Answer 3

k thanks malevolence, I wish I could keep you on retainer, haha

Answer 4

\[\int_0^{54}\int_{-1}^{1}(1-y^2) - (y^2 - 1) dydx \]

Answer 5

I think that's how you start it anyway.

Answer 6

haha wow, I was way off

Answer 7

\[= 108\int_{-1}^1 1-y^2dy\]

Answer 8

We find the bounds on y by finding the y values for where the two curves intersect:

\[1-y^2 = y^2-1 \implies 2y^2 = 2 \implies y = \pm 1\]

Answer 9

We are given the bounds on x.

Answer 10

yup 144

Answer 11

was right

Answer 12

I used the wrong bounds for y and I think I did the first intergal wrong, haha. Thanks for the help polpak!

Answer 13

Sure thing