Find the volume of the solid generated by revolving the region about the given line.

The region in the first quadrant bounded above by the line y=√2, below by the curve y=2sinx, 0≤x≤π, and on the left by the y-axis, about the line y=2.

Question

Find the volume of the solid generated by revolving the region about the given line.

The region in the first quadrant bounded above by the line y=√2, below by the curve y=2sinx, 0≤x≤π, and on the left by the y-axis, about the line y=2.

anonymous · Answer

I'll give it a try: y=2 sin x, y = sq rt 2; (1) 2 sin x = sq rt 2; therefore x = pi/4. Radius big circle 2, radius small 2 - 2 sin x. Therefore, V = integrand from 0 to pi/4 of (2^2 -[2 - 2 sin x]^2)pi dx. I will ask around tomorrow if I am right. Been a while since I did it. Btw this is washer method.