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 ∫ 2 6 ∫ 1 4 x 2 d x d y 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 ∫ 2 6 ∫ 1 4 x 2 d x d y Let us first compute the indefinite integral Applying the power rule, we get ∫ 1 4 x 2 d x =

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.1, Problem 25E

To determine

The value of the iterated integral $\int_{2}^{6} \int_{1}^{4} x^{2} d x d y$

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Chapter 16.1, Problem 24E

Chapter 16.1, Problem 26E

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