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

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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

Mathematics
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Anyone?
Disk method seems good to me.
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.

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