Explanation Given info: The triple integral in cartesian form is given. ∫ − 2 2 ∫ − 4 − x 2 4 − x 2 ∫ 0 4 − x 2 − y 2 e − ( x 2 + y 2 + z 2 ) 3 2 d z d y d x The range of z is from 0 to 4 − x 2 − y 2 . The range of y is from − 4 − x 2 to + 4 − x 2 and x from − 2 to 2 . Calculation: 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 Write the given triple integral in spherical coordinate In spherical coordinates write the range of difference variables, r varies from 0 to 2 , ϕ varies from 0 to 2 π and θ varies from 0 to π . Now, write the given triple integral in spherical coordinate. ∫ 0 2 π ∫ 0 π ∫ 0 2 e − r 3 ( r 2 sin ϕ ) d r d ϕ d θ (1) First evaluate the integral with variable r : Take t = t 2 and differentiate it, d t = 3 r 2 d r r 2 d r = d t 3 Find the limits for integration as, variable is changes. When r = 2 , t = 8 and when r = 0 , t = 0 . Write the triple integral equation (1) in term of t , ∫ 0 2 π ∫ 0 π ∫ 0 8 e − t d t 3 sin ϕ d ϕ d θ Now integrate with respect to t ,

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, Problem 37CRE

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To convert the given triple integral into spherical coordinate and evaluate the integral.

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Chapter 16, Problem 36CRE

Chapter 16, Problem 38CRE

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Prob. 37E Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 44E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Prob. 47E Ch. 16.5 - Prob. 48E Ch. 16.5 - Prob. 49E Ch. 16.5 - 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Prob. 26CRE Ch. 16 - Prob. 27CRE Ch. 16 - Prob. 28CRE Ch. 16 - Prob. 29CRE Ch. 16 - Prob. 30CRE Ch. 16 - Prob. 31CRE Ch. 16 - Prob. 32CRE Ch. 16 - Prob. 33CRE Ch. 16 - Prob. 34CRE Ch. 16 - Prob. 35CRE Ch. 16 - Prob. 36CRE Ch. 16 - Prob. 37CRE Ch. 16 - Prob. 38CRE Ch. 16 - Prob. 39CRE Ch. 16 - Prob. 40CRE Ch. 16 - Prob. 41CRE Ch. 16 - Prob. 42CRE Ch. 16 - Prob. 43CRE Ch. 16 - Prob. 44CRE Ch. 16 - Prob. 45CRE Ch. 16 - Prob. 46CRE Ch. 16 - Prob. 47CRE Ch. 16 - Prob. 48CRE Ch. 16 - Prob. 49CRE Ch. 16 - Prob. 50CRE Ch. 16 - Prob. 51CRE Ch. 16 - Prob. 52CRE Ch. 16 - Prob. 53CRE Ch. 16 - Prob. 54CRE Ch. 16 - Prob. 55CRE Ch. 16 - Prob. 56CRE Ch. 16 - Prob. 57CRE Ch. 16 - Prob. 58CRE Ch. 16 - Prob. 59CRE Ch. 16 - Prob. 60CRE Ch. 16 - Prob. 61CRE

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To convert the given triple integral into spherical coordinate and evaluate the integral.

Solution Summary: The author explains how to convert the given triple integral into spherical coordinate and evaluate it.

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To convert the given triple integral into spherical coordinate and evaluate the integral.

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Chapter 16 Solutions