The region bounded by y=x^8 and y=sin(πx/2) is rotated about the line x=−5.
Using cylindrical shells, set up an integral for the volume of the resulting solid.

Question

The region bounded by y=x^8 and y=sin(πx/2) is rotated about the line x=−5. 
Using cylindrical shells, set up an integral for the volume of the resulting solid.

anonymous · Answer

here's what i have so far 

$$2\pi \int\limits_{0}^{1}(x+5)(\sin(\pi x/2)-x^8)$$

$$2\pi \int\limits_{0}^{1}-x^9-5x^8+xsin(\pi x /2)+5\sin(\pi x/2)$$

$$2\pi[(-x/10)-(5x^9/9)(-2\pi/x)(cos(\pi x/2))+(4/\pi^2)(sin(\pi x/2))-(10/\pi) (cos(\pi x/2))]$$

from 1 to 0, but the math doesn't work cause i can't divide by zero..$$-2\pi/x \cos(\pi x/2)$$ would be undefined making the whole thing undefined, right?