Calculate the volume of solid formed by revolving about the line y=1 the region bounded by the parabola x²=4y and that line. Take the rectangular elements of the area parallel to the axis of revolution.
Point of intersection of y=1
Since x2=4y, then; y=1 and x=2
Hence integration is to be carried out be between x=2 and y=1
Line is above the curve
Taking vertical strips of width dx and rotating about x-axis we the volume generated as
Hence Volume V=π∫(2x²-x⁴)
=π(9.429/1)=9.429π cubic units