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Chapter 6: Q. 21 (page 510)

Each of the definite integrals in Exercises 19鈥�24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.

蟺鈭�13(x2-2x+1)dx

Short Answer

Expert verified

The required region is shown as,

Step by step solution

01

Step 1. Given Information  

The given integral is 蟺鈭�13(x2-2x+1)dx

02

Step 2. Explanation  

The given integral is of the form 蟺鈭�ab(f(x))2dx which represents the volume of a solid formed by rotating the region bound by f(x) and x-axis in the interval [a,b] around x-axis.

On comparing the given region with the above region, we have,

f(x)=x2-2x+1intheinterval[1,3]

Factor the quadratic expression inside the radical sign to simplify it

f(x)=x2-2x+1=(x-1)2=x-1

The simplified function represents the straight line.

Plot the graph of the function and identify the region between the intervals.

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