Q. 17 - Calculus

Question

Show that the integrals from Exercises 13 and 16 evaluate

to the same quantity.

Step-by-Step Solution

Answer

The solid of revolution, the shell method and the method of polar coordinates represent the same volume generated by the revolution of curve $z=f\left(x\right)$ about $z$ - axis.

Step 1 Given Information

The objective of this problem is to show that problems 13 to 16 represent the volume of the solid of revolution obtained when the region bounded above by the graph of $f$ and bounded below by $x$ - axis on the interval $[0, b]$ is rotated about the $z$-axis.

Step 2 Calculation

The solid of revolution, the shell method and the method of polar coordinates represent the same volume generated by the revolution of curve $z=f\left(x\right)$ about $z$ - axis.