Explanation Given info: The volume of the solid bounded by y = x 2 , x = y 2 , z = x + y + 5 , and z = 0 Concept used: This shaded area is lower bounded by z = 0 and upper bounded by z = x + y + 5 . Volume of bounded solid ∫ ∫ w ∫ d v d v = d x d y d z Calculation: First find the point of intersection of curve y = x 2 and x = y 2 y = x 2 ----------- ( i ) x = y 2 ------------- ( ii ) Putting the value of y from ( i ) in ( ii ) x = ( x 2 ) 2 x 4 − x = 0 x = ( x 3 − 0 ) = 0 x = 0 or x 3 = 1 x = 0 or x = 1 Limit of z 0 ≤ z ≤ x + y + 5 Limit of y (From shaded region) x 2 ≤ y x Limit of x (From shaded region) 0 ≤ x ≤ 1 Volume = ∫ ∫ w ∫ d v = ∫ 0 1 ∫ x 2 x ∫ 0 x + y + 5 d z d y d x integrating w .r .t z = ∫ 0 1 ∫ x 2 x [ ∫ 0 x + y + 5 d z ] d y d x ( rewrite the expression ) = ∫ 0 1 ∫ x 2 x [ z ] 0 x + y + 5 d y d x ( putting the limit of z ) = ∫ 0 1 ∫ x 2 x ( x + y + 5 ) d y d x integrating w ...

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.3, Problem 20E

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Find the volume of the solid in $R^{3}$ bounded by $y = x^{2}, x = y^{2}, z = x + y + 5, and z = 0$

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Chapter 16.3, Problem 19E

Chapter 16.3, Problem 21E

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Chapter 16 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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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Find the volume of the solid in R 3 bounded by y = x 2 , x = y 2 , z = x + y + 5 , and z = 0

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Find the volume of the solid in $R^{3}$ bounded by $y = x^{2}, x = y^{2}, z = x + y + 5, and z = 0$

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Chapter 16 Solutions

Find the volume of the solid in R 3 bounded by y = x 2 , x = y 2 , z = x + y + 5 , and z = 0

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Find the volume of the solid in R3bounded by y=x2,x=y2,z=x+y+5, and z=0

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Find the volume of the solid in $R^{3}$ bounded by $y = x^{2}, x = y^{2}, z = x + y + 5, and z = 0$