Question

find the volume of the solid generated by revolving the region about the given line. the region in the first quadrant bound above by the line y=1, below by the curve y=√(sin5x) ,and on the left by the y-axis, above the line y=-1

Answer 1

What is the "given line" that the solid volume revolves around?

Answer 2

Should the word "above" in the last line be "about"? Then the question would make sense.

Answer 3

using washers, the volume is

∫[0,π/10] π R^2-r^2 dx
where R=2 and r = √(sin5x) + 1

v = ∫[0,π/10] π (4 - (√(sin5x)+1)^2) dx


I think you are in trouble.

∫√(sin5x) dx

cannot be evaluated using elementary functions.