## anonymous 5 years ago Please someone.. I just need to know which method to use here.. Find the volume of the solid generated by revolving the described region about the given axis: The region in the first quadrant bounded above by the line y=4 and by the curve y=4sin(x) for the interval 0≤x≤π2 about the line y=4

1. anonymous

Anyone?

2. TuringTest

Disk method seems good to me.

3. TuringTest

I'm gonna assume your interval is$0\le x\le\frac\pi 2$your graph will be|dw:1327539383308:dw|it looks like the area of each disk will be$dA=\pi r^2=\pi(4-4\sin x)^2dx=16\pi(1-2\sin x+\sin^2x)dx$Being a little clever here we can use a trig identity and this becomes$dA=16\pi[1-2\sin x+\frac1 2(1-\cos(2x)]dx$$dA=16\pi[\frac3 2-2\sin x-\cos(2x)]dx$which we can integrate over our interval with a simple u-substitution.