Find the volume of the solid S obtained by rotating the region bounded by the curve y=sin(x^2) and the x-axis from x=0 to x=√π about the y-axis

Answer 1

his problem is most easily worked using the shell method

V = 2π ∫ x sin(x² ) dx with limits 0 and π^.5

The anti derivative is -(1/2) cos(x²) so the answer is V = 2π