Use the washer method to find the volume of the solid generated by revolving the region bounded by the parabola y=x^4 and the line y=8x about the y-axis.

Question

anonymous · Answer

did you get stuck somewhere?

anonymous · Answer

not really, im pretty sure i got the entire thing wrong

anonymous · Answer

http://www.wolframalpha.com/input/?i=Plot%5Bx%5E4%2C8x%5D&t=crmtb01

anonymous · Answer

is it the first graph or the one on the bottom?

anonymous · Answer

x^4, and 8x

anonymous · Answer

isnt there more to the problem tho? i think there needs to be limits of integration, integrand, and the correct volume

anonymous · Answer

We have to integrate with respect to Y since we want to use washer method

y  from 0 to 16

anonymous · Answer

y=x^4
y=8x

x= y^1/4

x= 1/8

anonymous · Answer

x=1/8 y

anonymous · Answer

$$\pi  \int _0^{16}\left(\sqrt[4]{y}\right)^2-\left(\frac{y}{8}\right)^2dy$$

zarkon · Answer

the problem is nicer with the shell method

$$\int\limits_{0}^{2}2\pi x(8x-x^4)dx$$

zarkon · Answer

both give the same answer...so it is a nice way to check yourself.

anonymous · Answer

but my teacher wants us to use the washer method

anonymous · Answer

the first one is washer

zarkon · Answer

yes...the first is washers...I just prefer shells for this problem :)

zarkon · Answer

I get $\displaystyle\frac{64\pi}{3}$ doing it either way

anonymous · Answer

alrite thanks you guys