Find the volume of the solid obtained by rotating the region bounded by y=x^2 , y = 0, and x = 2,, about the y-axis. I get 6.2831853, but its wrong. Help me understand where I went wrong, please.

Question

Find the volume of the solid obtained by rotating the region bounded by y=x^2 , y = 0, and x = 2,, about the y-axis.  I get 6.2831853, but its wrong. Help me understand where I went wrong, please.

anonymous · Answer

x=sqrty intgrated[0,2] pi(y)dy = 6.2831853

campbell_st · Answer

well not quite

you are rotating about the y-axis so substitute x =2 to find the corresponding y value


|dw:1389762767444:dw|

then its 

$$V=\pi \int\limits_{0}^{4} x^2 dy$$

you know 

$$y = x^2$$

so substitute and you have 

$$V = \pi \int\limits_{0}^{4}(y) dy$$

hopefully you can get the rest from here...