Explanation Given: The triple integral which is improper. ∫ ∫ ∫ ( x 2 + y 2 + z 2 + 1 ) − 2 d V = π 2 Calculation: Convert into cylindrical coordinates. Let x = r sin θ cos ϕ , y = r sin θ sin ϕ , z = r cos θ Then d V = r 2 sin θ d r d θ d φ 0<φ<2п 0<r<R 0<Ɵ<п The integrand becomes 1 ( r 2 + 1 ) 2 The given integral = ∫ 0 R ∫ 0 2 π ∫ 0 π 1 ( r 2 + 1 ) 2

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.4, Problem 58E

To determine

Q.No

58)

To find:

$\int \int \int (x^{2} + y^{2} + z^{2} + 1)^{- 2} d V = π^{2}$

Where the integration is done all over R³

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Chapter 16.4, Problem 57E

Chapter 16.4, Problem 59E

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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Q.No 58) To find: ∫ ∫ ∫ ( x 2 + y 2 + z 2 + 1 ) − 2 d V = π 2 Where the integration is done all over R 3

Solution Summary: The author analyzes how the given integral converges to 2 when R is infinity.

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Q.No

58)

To find:

$\int \int \int (x^{2} + y^{2} + z^{2} + 1)^{- 2} d V = π^{2}$

Where the integration is done all over R³

Want to see the full answer?

Chapter 16 Solutions

Q.No 58) To find: ∫ ∫ ∫ ( x 2 + y 2 + z 2 + 1 ) − 2 d V = π 2 Where the integration is done all over R 3

Solution Summary: The author analyzes how the given integral converges to 2 when R is infinity.

Videos

Q.No 58) To find: ∫∫∫(x2+y2+z2+1)−2dV=π2 Where the integration is done all over R3

Want to see the full answer?

Chapter 16 Solutions

Q.No

58)

To find:

$\int \int \int (x^{2} + y^{2} + z^{2} + 1)^{- 2} d V = π^{2}$

Where the integration is done all over R³