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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Calculate the iterated integral.

25. 0 1 0 1 v ( u + v 2 ) 4 d u d v

To determine

To estimate: The value of given iterated integral.

Explanation

Calculation:

First, compute the integral with respect to u.

0101v(u+v2)4dudv=01[15v(u+v2)5]01dv

Apply the limit value for u,

0101v(u+v2)4dudv=1501v[(v2+1)5(0+v2)5]dv=1501[v(v2+1)5v11]dv=1501v(v2+1)5dv1501v11dv

Compute the integral with respect to v.

To integrate 1501v(v2+1)5dv , substitute, t=1+v2 .

Then, dt=2vdv

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Chapter 15 Solutions

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