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 ...

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ISBN: 9781319050733

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

CALCULUS (CLOTH)

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

Solution Summary: The author explains how to determine the volume of the solid in R 3 bounded by y = x 2.

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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

Solution Summary: The author explains how to determine the volume of the solid in R 3 bounded by y = x 2.

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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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Chapter 16 Solutions

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