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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
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

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TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.0Disk method seems good to me.

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.0I'm gonna assume your interval is\[0\le x\le\frac\pi 2\]your graph will bedw:1327539383308:dwit looks like the area of each disk will be\[dA=\pi r^2=\pi(44\sin x)^2dx=16\pi(12\sin x+\sin^2x)dx\]Being a little clever here we can use a trig identity and this becomes\[dA=16\pi[12\sin x+\frac1 2(1\cos(2x)]dx\]\[dA=16\pi[\frac3 22\sin x\cos(2x)]dx\]which we can integrate over our interval with a simple usubstitution.
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