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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 7.8, Problem 43E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Problem 43E
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Problem 69E
Problem 70E
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Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Sketch the region and find its area (if the area is finite).

S = { ( x , y ) | x ≥ 1 ,   0 ≤ y ≤ 1 / ( x 3 + x ) }

To determine

To sketch:

the given region, and find its area if the area is finite.

Explanation

Given:

S={(x,y)|x≥1,0≤y≤1/(x3+x)}

Formulae used: Area under the curve y=f(x) in the interval [a,b] is A=∫abf(x)dx

Consider S={(x,y)|x≥1,0≤y≤1/(x3+x)}

Plot curves where x∈[1,∞],y∈[0,1/(x3+x)] and get,

Now, from the graph f(x)=1x3+x in the interval [1,∞] the area appear finite.

Use the formulae to get the area under the cure, as

A=∫1∞1x3+xdx

Decompose the above expression into partials fractions and get,

1x3+x=Ax+Bx+Cx2+1=A(x2+1)+(Bx+C)(x)x3+x1=Ax2+A+Bx2+Cx0x2+0x+1=(A+B)x2+Cx+A

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Explain how holding a participant variable such as gender constant prevents the variable from becoming a confou...

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For a distribution with a mean of 70 a. If the distribution had a standard deviation of 4, would a score of 82 ...

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A zoo has categorized its visitors into three categories: member, school, and general. The member category refe...

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Find the slope and the yintercept of the graph of each line. 3x4y=14

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Amtracks Downeaster train leaves Biddeford, Maine, at 6:42A.M., Mondays through Fridays. It arrives at Boston a...

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In exercise 6, data were given on the average number of passing yards per attempt (Yds/ Att), the number of int...

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