Disk Method (Rotation about x-axis)The volumeof solid of revolution generated by rotating a plan region about x-axis as shown below isy∫=badxxRV)(2πDisk of radius R(x).pk[email protected]xxybax)(xR4[email protected]
Example:The region lying in the first quadrant between the curvex=y2and lines y=0 and x=4 is revolved about the x-axis togenerate a solid. Find its volume..pk[email protected]5[email protected]
xyy(29π)(2=∫dxxRVba40x)(xRxy=xy=Radius of the disk will bexxR=)(Volume of the solid of revolution.pkxπππ840402===∫∫xdxdxxDisk of radius R(x)[email protected]6[email protected]
Example:The region lying between the curve x=3-y2and lines x=3and y=√3is revolved about the line y=√3to generate a solid. Find itsvolume.