Explanation Given: The integral is ∫ 0 1 ∫ 3 6 x x 2 + 3 y d x d y . Approach: For evaluating double integral we do integration of inner integral first and then outer integral in given order of integration. Calculation: Given integral is ∫ 0 1 ∫ 3 6 x x 2 + 3 y d x d y On integrating inner integral with respect to x and outer integral with respect to y , ∫ 0 1 ∫ 3 6 x x 2 + 3 y d x d y = ∫ 0 1 ∫ 3 6 x ( x 2 + 3 y ) 1 2 d x d y = ∫ 0 1 1 2 [ ( x 2 + 3 y ) 1 2 + 1 1 2 + 1 ] 3 6 d y = ∫ 0 1 1 3 [ ( x 2 + 3 y ) 3 2 ] 3 6 d y = ∫ 0 1 1 3 [ ( 6 2 + 3 y ) 3 2 − ( 3 2 + 3 × y ) 3 2 ] d y = ∫ 0 1 1 3 [ ( 36 + 3 y ) 3 2 − ( 9 + 3 y ) 3 2 ] d y = 1 3 [ 1 3 × ( 36 + 3 y ) 3 2 + 1 3 2 + 1 − 1 3 × ( 9 + 3 y ) 3 2 + 1 3 2 + 1 ] 0 1 Simplify further,

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Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 9.5, Problem 13E

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The integral is ∫01∫36xx2+3ydxdy

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Chapter 9.5, Problem 12E

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The integral is ∫ 0 1 ∫ 3 6 x x 2 + 3 y d x d y

Solution Summary: The author calculates the value of the integral by integrating inner and outer integrals in the same order.

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To find: The integral is ∫01∫36xx2+3ydxdy

Want to see the full answer?

Chapter 9 Solutions

To find:

The integral is ∫01∫36xx2+3ydxdy