Explanation In order to obtain the double integral, integrate the inner integral first. ∫ y y 2 1 y 2 − x 2 d x = ∫ y y 2 1 y 1 − ( x y ) 2 d x [ ∵ ∫ 1 a 2 − x 2 d x = sin − 1 x a + C ] = [ sin − 1 x y ] y y 2 = [ sin − 1 y 2 y ] − [ sin − 1 y y ] = sin − 1 y − π 2 Now, obtain the outer integral with the help of the result of inner integral as follows. ∫ 0 1 2 ( sin − 1 y − π 2 ) d y = ∫ 0 1 2 sin − 1 y d y − π 2 ∫ 0 1 2 d y = [ y sin − 1 y + 1 − y 2 ] 0 <

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Chapter 29.4, Problem 18E

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The value of the double integral ∫012∫yy21y2−x2dxdy.

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Chapter 29.4, Problem 17E

Chapter 29.4, Problem 19E

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Chapter 29 Solutions

Basic Technical Mathematics

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

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The value of the double integral ∫ 0 1 2 ∫ y y 2 1 y 2 − x 2 d x d y .

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The value of the double integral ∫012∫yy21y2−x2dxdy.

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Chapter 29 Solutions