Problem 37E

Geometry problems

Use a table of integrals to solve the following problems.

The region bounded by the graph of and the x-axis on the interval [0, 12] is revolved about the y-axis. What is the volume of the solid that is formed?

Problem 37E

Geometry problems Use a table of integrals to solve the following problems.

The region bounded by the graph of and the x-axis on the interval [0, 12] is revolved about the y-axis. What is the volume of the solid that is formed?

Solution

Step 1

In this problem we have to find the volume of the solid bounded by the region , and the x-axis on the interval [0,12] is revolved about y-axis.

We shall use shell method to find the volume.

Shell method : If R is the region under the curve y = f(x) on the interval [a, b], then the volume of the solid obtained by revolving R about the y-axis is