   Chapter 8.8, Problem 68E

Chapter
Section
Textbook Problem

Area and Volume In Exercises 67 and 68, consider the region satisfying the inequalities (a) Find the area of the region. (b) Find the volume of the solid generated by revolving the region about the x -axis. (c) Find the volume of the solid generated by revolving the region about the y -axis. y ≤ 1 x 2 , y ≥ 0 ,   x ≥ 1

(a)

To determine

To calculate: The area of the region bounded by the inequalities y1x2, y0, x1.

Explanation

Given:

The region is satisfying the inequalities

y1x2, y0, x1

Formula used:

xndx=[xn+1n+1]+c

Area of a region that is bound by the graph of f(x) in the interval [a,b] can be determined as

A=abf(x)dx

Calculation:

From the provided inequalities of x and y, f(x)=1x2 the limit of the integral will be [1,)

(b)

To determine

To calculate: The volume of the solid that is createdby revolving the region about x-axis.

(c)

To determine

To calculate: The volume of the solid created by revolving the region about y-axis

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