Explanation Riemann Sum is defined as the approximation of the integral by computing the finite sum. Given: The function is f ( x , y ) = x y and rectangle is given as R = [ 1 , 3 ] × [ 1 , 2 .5 ] Formula: If the interval [ a , b ] is divided into n sub intervals, then the length of each side is given as Δ x = b − a n Riemann Sum is given as S = ∑ i = 1 n ∑ j = 1 m f ( x i ) Δ x i Calculation: Given that the partition is regular, thus each sub rectangle will have same length and breadth. Sides of the rectangles are given as follows: Δ x = 3 − 1 4 = 2 4 = 1 2 = 0.5 Δ y = 2 .5 − 1 3 = 1.5 3 = 0 .5 Area of sub rectangle, Δ A = 0.5 × 0.5 = 0.25 The rectangle and sub rectangles will be displayed as follows The upper right vertices of sub rectangles are the below points P 11 = ( 1.5 , 1.5 ) P 21 = ( 2 , 1.5 ) P 31 = ( 2.5 , 1.5 ) P 41 = ( 3 , 1.5 ) P 12 = ( 1.5 , 2 ) P 22 = ( 2 , 2 ) P 32 = ( 2.5 , 2 ) P 42 = ( 3 , 2 ) P 13 = ( 1.5 , 2 .5 ) P 23 = ( 2, 2 .5 ) P 33 = ( 2 .5, 2 .5 ) P 43 = ( 3, 2 ...

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Question

Chapter 15.1, Problem 1E

To determine

Compute the Riemann sum $S_{4, 3}$ in order to estimate the double integral of the function $f (x, y) = x y$ over $R = [1, 3] \times [1, 2 .5]$ using a regular partition and upper right vertices of the sub rectangles as sample points.

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Chapter 15.1, Problem 6PQ

Chapter 15.1, Problem 2E

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Chapter 15 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 15.1 - Prob. 1PQ Ch. 15.1 - Prob. 2PQ Ch. 15.1 - Prob. 3PQ Ch. 15.1 - Prob. 4PQ Ch. 15.1 - Prob. 5PQ Ch. 15.1 - Prob. 6PQ Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E

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Knowledge Booster

Compute the Riemann sum S 4 , 3 in order to estimate the double integral of the function f ( x , y ) = x y over R = [ 1 , 3 ] × [ 1 , 2 .5 ] using a regular partition and upper right vertices of the sub rectangles as sample points.

Compute the Riemann sum S4, 3 in order to estimate the double integral of the function f(x, y) = xyover R = [1, 3] × [1, 2.5]using a regular partition and upper right vertices of the sub rectangles as sample points.

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Chapter 15 Solutions

Compute the Riemann sum $S_{4, 3}$ in order to estimate the double integral of the function $f (x, y) = x y$ over $R = [1, 3] \times [1, 2 .5]$ using a regular partition and upper right vertices of the sub rectangles as sample points.