Question

the region bounded by the curves x=2y² and x=y³ then use the shell method to find the volume of the solid generated by revolving this region about the y -axis.

Answer 1

To find the volume of the solid generated by revolving the region bounded by the given curves, use the shell method.

Step-by-step explanation:

To find the volume of the solid generated by revolving the region bounded by the curves x=2y² and x=y³ about the y-axis, we can use the shell method.

The shell method involves integrating the circumference of a cylindrical shell multiplied by its height. In this case, the height is the difference between the two curves, which is y³ - 2y².

Using the shell method, the volume is given by the integral from 0 to the y-coordinate of the point of intersection of the two curves of 2πy(y³ - 2y²)dy.