Explanation Let there be a continuous function f ( x , y ) on R = [ a , b ] × [ c , d ] , then the below integrals are referred to as iterated integrals. ∬ R f ( x , y ) d A = ∫ a b ∫ c d f ( x , y ) d y d x = ∫ c d ∫ a b f ( x , y ) d x d y Given: An iterated integral as ∫ 1 3 ∫ 0 2 x 3 y d y d x Formula Used: Integration of the below functions: 1. Constant Function: ∫ a d x = a x + c 15. Variable Function: ∫ x d x = x 2 2 + c 30. Reciprocal Function: ∫ 1 x d x = l n | x | + c 45. Exponential Function: ∫ e x d x = e x + c 59. Trigonometric Function: a. ∫ s i n ( x ) d x = - c o s ( x ) + c q. ∫ c o s ( x ) d x = s i n ( x ) + c 60. Sum Rule of Derivative: ∫ ( f + g ) d x = ∫ f d x + ∫ g d x 78. Difference Rule of Derivative: ∫ ( f - g ) d x = ∫ f d x - ∫ g d x Calculation: The given problem is ∫ 1 3 ∫ 0 2 x 3 y d y d x Let us first compute the indefinite integral ∫ 0 2 x 3 y d y ∫ 0 2 x 3 y d y = x 3 ∫ 0 2 y d y Applying the power rule, we get, ∫ 0 2 x 3 y d y = x 3 y 1 + 1 1 + 1 | 0 2 ∫ 0 2 x 3 y d...

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.1, Problem 19E

To determine

The value of the iterated integral $\int_{1}^{3} \int_{0}^{2} x^{3} y d y d x$

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Chapter 16.1, Problem 18E

Chapter 16.1, Problem 20E

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The value of the iterated integral ∫ 1 3 ∫ 0 2 x 3 y d y d x

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