Explanation Given information: ∫ − 1 − 1 ∫ x 2 x 2 + y d y d x Formula Used: ∫ x n d x = x n + 1 n + 1 + C Calculation: The average value for a double integration is given by f a v g = 1 A R ∫ ∫ R f x , y d A So, let us find the value for the double integration first and then divide it by the area of region bounded by the bounds of x and y , to find the average value. It has been given that ∫ − 1 − 1 ∫ x 2 x 2 + y d y d x . Integrate with respect to y ∫ − 1 1 x 2 y + y 2 2 x 2 d x ∫ x n d x = x n + 1 n + 1 + C = ∫ − 1 1 2 x 2 + 2 − x 3 + x 2 2 d x =

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Chapter 6.6, Problem 23E

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Find the average value of the function in the integrand over the region defined by the bounds of integration for the double integration ∫−1−1∫x2x2+ydydx .

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Chapter 6.6, Problem 22E

Chapter 6.6, Problem 24E

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Find the average value of the function in the integrand over the region defined by the bounds of integration for the double integration ∫ − 1 − 1 ∫ x 2 x 2 + y d y d x .

Solution Summary: The author calculates the average value of the function in the integrand over the region defined by the bounds of integration for the double integration.

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Find the average value of the function in the integrand over the region defined by the bounds of integration for the double integration ∫−1−1∫x2x2+ydydx .

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