To determine Calculate the value of iterated integral. Explanation Given information: The integral is ∫ − 1 2 ∫ 1 2 x ln y d y d x . Calculation: Express the integral as follows: ∫ − 1 2 ∫ 1 2 x ln y d y d x (1) Integrate Equation (1) with respect to x and keep y as constant. ∫ − 1 2 ∫ 1 2 x ln y d y d x = ∫ − 1 2 { ∫ 1 2 x ln y d y } d x (2) Determine the value of x ∫ ln y d y using integration by parts; Express the formula for integration by parts as follows: ∫ f g ′ = f g − ∫ f ′ g (3) Express the value of f as follows: f = ln ( y ) Express the value of f ′ as follows: f ′ = 1 y Express the value of g as follows: g = y Express the value of g ′ as follows: g ′ = d y Substitute ln ( y ) for f , y for g , and 1 y for f ′ in Equation (3)

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Chapter 14.1, Problem 14E

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Calculate the value of iterated integral.

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Ch. 14.1 - In Exercises 1-14. evaluate the iterated...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated integral....Ch. 14.1 - In Exercises 1-14, evaluate the iterated...Ch. 14.1 - In Exercises 1-14, evaluate the iterated integral....Ch. 14.1 - Prob. 10E

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