what is the volume of the solid generated by rotating about the y-axis & sinx
what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=$\displaystyle \pi$.
what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=$\displaystyle \pi$.
cylindrical shells may be the way to go on this ...
what do you get for the integral set up to find the volume?
what is the volume of the solid generated by rotating about the y-axis the region enclosed by y=sinx and the x-axis, from x=0 to x=$\displaystyle \pi$.
Simply use the method of cylindrical shells:
$\displaystyle V = 2\pi\int_0^\pi x(\sin x)dx$
$\displaystyle V = 2\pi\left[sin x - xcos x\right]_0^\pi$