Question

Find the volume of the solid generated by revolving the region bounded by the given lines and curves

Answer 1

Question:

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis: y=x2,y=0,x=0, and x=4.y=x2,y=0,x=0, and x=4.

Volume of Solid of Revolution:

In this problem, we are asked to find the volume of a solid formed by revolving a plain region about the x-axis. To accomplish this task, we will use the formula for volume. The formula for a solid generated by a curve (y) bounded by the x-axis and the x values of a and b, which revolves about the x-axis is:

V=π∫bay2dxV=π∫aby2dx

Answer and Explanation:

To figure the volume, let's first apply the given curve (y) to the formula:

V=π∫40(x2)2dx=π∫40x4V=π∫04(x2)2dx=π∫04x4

Now we can integrate and evaluate:

V=πx55|40=π455V=πx55|04=π455

V=1024π5≈643.40