Question

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

Answer 1

Anyone?

Answer 2

Disk method seems good to me.

Answer 3

I'm gonna assume your interval is\[0\le x\le\frac\pi 2\]your graph will beit 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.