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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Let be the region bounded by the curves y = 1 x 2 and y = x 6 x + 1 . Estimate the following quantities.

(a) The x -coordinates of the points of intersection of the curves

(b) The area of

(c) The volume generated when . is rotated about the x -axis

(d) The volume generated when , is rotated about the y -axis

To determine

a)

To estimate:

The x  coordinates of the points of intersection of the curves.

Explanation

1) Concept:

Draw the graph of the given curves, and find the point of intersection.

2) Given:

y=1-x2,y=x6-x+1

3) Calculation:

The equation of curve is

y=1-x2,y=x6-x+1

Draw the given curves

To determine

b)

To estimate:

The area of R

To determine

c)

To estimate:

The volume obtained by rotating R  about x  axis.

To determine

d)

To estimate:

The volume obtained by rotating R  about y   axis.

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