Volumes by Cylindrical shells (1 Viewer)

[qqmore]

Q. The Region R in the first quadrant such that y < / 4x^2 - x^4 is rotated about the y axis to form a solid of revolution. Use the method of decomposition into cylindrical shells to show the volume is 32 pie /3.

(< / = less than or equal to)
Hmm, how do you do this question? I keep getting 64pie/3 as the answer.

 

[malady]

vol= Int (0,2)[ 2(pi)xy] dx= 2(pi) Int (0,2)[x(4x^2-x^4)dx= 32(pi)/3

 

[qqmore]

thanks alot..... just realised i integrated it wrong =(..

 

[ronnknee]

Here's the working out if anyone else needs it:

dV
= 2 pi xy dx
= 2 pi x(4x^2 - x^4) dx
= 2 pi (4x^3 - x^5) dx

V
= 2 pi INT([2, 0] 4x^3 - x^5)
= 2 pi [4x^4 / 4 - x^6][2, 0]
= 2 pi [32 - 64/3]
= 32 pi / 3