Explanation Given: f ( x , y ) = 6 x y − x 2 ; bounded below by x 2 and above by x . Formula used: The integration formula ∫ x n d x = x n + 1 n + 1 . Calculation: To find the double integral first we have to find the points of the domain as 0 is bounded below by x 2 and above by x . Hence y varies from x 2 to x . Now, to find the points of ‘ x’ we need to find where y = x 2 and y = x intersect putting y = x in y = x 2 we have x = x 2 x = x 4 x = 0 , 1 Hence, x varies from’0’ to 1 Now to find ∫ 0 1 ∫ x 2 x ( 6 x y − x 2 ) d y d x First, calculate the inner integral by treating ‘ x’ as constant S ( x ) = ∫ x 2 x ( 6 x y − x 2 ) d y

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 21E

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Compute the double integral of f(x,y)=6xy−x2 over domain 0 which is bounded below by x2 and above by x

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Chapter 16.2, Problem 20E

Chapter 16.2, Problem 22E

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Compute the double integral of f ( x , y ) = 6 x y − x 2 over domain 0 which is bounded below by x 2 and above by x

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Compute the double integral of f(x,y)=6xy−x2 over domain 0 which is bounded below by x2 and above by x

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Chapter 16 Solutions