Explanation Given info: The integral function in Cartesian form is f ( x , y , z ) = x 2 + y 2 + z 2 . It is confined in a region 1 to 4 . Calculation: First convert the triple integral in spherical coordinates. The variables in spherical coordinate are, x = r sin ϕ cos θ , y = r sin ϕ sin θ and z = r cos ϕ Here, r = x 2 + y 2 + z 2 In spherical coordinates the range of difference variables, r varies from 1 to 2 , θ varies from 0 to 2 π and ϕ varies from 0 to π . So, the triple integral using function and the bound of region using spherical coordinate, ( r , θ , ϕ ) is, ∫ 0 2 π ∫ 0 π ∫ 1 2 f ( r , θ , ϕ ) d V Substitute the value of function in spherical coordinate, I = ∫ 0 π ∫ 0 2 π ∫ 1 2 r 2 r 2 sin ϕ d r d θ d ϕ = ∫ 0 π ∫ 0 2 π ∫ 1 2 r 4 sin ϕ d r d θ d ϕ First evaluate the integral for variable r and substitute the limits...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16, Problem 36CRE

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To calculate the given triple integral of a given function over a region $1 \leq x^{2} + y^{2} + z^{2} \leq 4$ using spherical coordinates.

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Chapter 16, Problem 35CRE

Chapter 16, Problem 37CRE

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To calculate the given triple integral of a given function over a region 1 ≤ x 2 + y 2 + z 2 ≤ 4 using spherical coordinates.

Solution Summary: The author explains how to calculate the triple integral of a given function using spherical coordinates.

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To calculate the given triple integral of a given function over a region $1 \leq x^{2} + y^{2} + z^{2} \leq 4$ using spherical coordinates.

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Chapter 16 Solutions

To calculate the given triple integral of a given function over a region 1 ≤ x 2 + y 2 + z 2 ≤ 4 using spherical coordinates.

Solution Summary: The author explains how to calculate the triple integral of a given function using spherical coordinates.

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To calculate the given triple integral of a given function over a region 1≤x2+y2+z2≤4using spherical coordinates.

Want to see the full answer?

Chapter 16 Solutions

To calculate the given triple integral of a given function over a region $1 \leq x^{2} + y^{2} + z^{2} \leq 4$ using spherical coordinates.