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Chapter 6: Q. 16 (page 522)

Each of the definite integrals in Exercises 11鈥�16 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis, computed with the shell method. Find this region.

2蟺鈭�013y-3y2dy

Short Answer

Expert verified

The region is y=1-x3.

Step by step solution

01

Step 1. Given Information. 

We are given,

2蟺鈭�013y-3y2dy

02

Step 2. Finding the region.

Rewriting the integral 2蟺鈭�013y-3y2dyas,

2蟺鈭�013y-3y2dy=2蟺鈭�01y(3-3y)dy

The shell represented by the integral is,

2蟺ykf-1yk螖y

Compare 2蟺ykf-1yk螖ywith the function inside the integral 2蟺鈭�013y-3y2dyas,

x=3-3yy=1-x3

Therefore, the region is y=1-x3.

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