The solid for an integral π∫0πsinxdx which represents the volume of a solid
= x, y| 0≤x≤π, 0≤y≤sinx. Rotation about the x- axis
i. If the cross section is a disc and the radius of the disc is in terms of x or y, then area A=π radius2
ii. The volume of the solid revolution about the x-axis is
Given π∫0πsinxdx can be written as π∫0πsinx2dx
Compare this with expression for volume.
So the given expression is the volume of a solid with cross section a disc with radius sinx, and it is perpendicular to the axis of rotation x- axis.
So, the solid is obtained by rotating the area bounded by the line y=0 and the curve y= sinx, between x=0 and x=π about the x-axis.
This region can be written as
= x, y| 0≤x≤π, 0≤y≤sinx
Therefore, the integral
describes the volume of the solid obtained by rotating the region
= x, y| 0≤x≤π, 0≤y≤sinx of the xy- plane about the x- axis
The above integral describes the volume of the solid obtained by rotating the region
= x, y| 0≤x≤π, 0≤y≤sinx of the xy- planeabout the x- axis