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(xj, Y;) AA, whe i = 1 Approximate the integral f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum of the ith square. Evaluate the iterated integral and compare it with the approximation. x²y dy dx Step 1 The vertices of the rectangle are given as (0, 0), (4, 0), (4, 2), and (0, 2). As the x-coordinate varies from 0 to 4, the length of the rectangle is As the y-coordinate varies from 0 to 2, the breadth of the rectangle is

(xj, Y;) AA, whe i = 1 Approximate the integral f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum of the ith square. Evaluate the iterated integral and compare it with the approximation. x²y dy dx Step 1 The vertices of the rectangle are given as (0, 0), (4, 0), (4, 2), and (0, 2). As the x-coordinate varies from 0 to 4, the length of the rectangle is As the y-coordinate varies from 0 to 2, the breadth of the rectangle is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Approximate the integral f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum f(xj, Y;) AA; where (x;, y;) is the center i = 1 of the ith square. Evaluate the iterated integral and compare it with the approximation. 1 x²y dy dx Step 1 The vertices of the rectangle are given as (0, 0), (4, 0), (4, 2), and (0, 2). As the x-coordinate varies from 0 to 4, the length of the rectangle is As the y-coordinate varies from 0 to 2, the breadth of the rectangle is Therefore, the area of the rectangle is
Transcribed Image Text:Approximate the integral f(x, y) dA by dividing the rectangle R with vertices (0, 0), (4, 0), (4, 2), and (0, 2) into eight equal squares and finding the sum f(xj, Y;) AA; where (x;, y;) is the center i = 1 of the ith square. Evaluate the iterated integral and compare it with the approximation. 1 x²y dy dx Step 1 The vertices of the rectangle are given as (0, 0), (4, 0), (4, 2), and (0, 2). As the x-coordinate varies from 0 to 4, the length of the rectangle is As the y-coordinate varies from 0 to 2, the breadth of the rectangle is Therefore, the area of the rectangle is
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