Use the Midpoint Rule with m = n = 2 to estimate the value of the integral IL x - 3y?) da where EXAMPLE 3 R 2.2) R R SOLUTION In using the Midpoint Rule with m =n= 2, we evaluate f(x, y) = x - 3y2 at the centers of the four subrectangles shown in the figure. So 1, 71 = 5/4, and 2 - The area of each sub-rectangle is AA =| Thus 2 « - 3y) da = -1j-1 Video Example ) - (x1, 71) A + f(ã1, 72) AA + f(ã2, 71) aa + Mã2, ỹ2) A AA + - (-용) (□)· (-)을• (□)을 • (-꽃)을 Thus we have
Use the Midpoint Rule with m = n = 2 to estimate the value of the integral IL x - 3y?) da where EXAMPLE 3 R 2.2) R R SOLUTION In using the Midpoint Rule with m =n= 2, we evaluate f(x, y) = x - 3y2 at the centers of the four subrectangles shown in the figure. So 1, 71 = 5/4, and 2 - The area of each sub-rectangle is AA =| Thus 2 « - 3y) da = -1j-1 Video Example ) - (x1, 71) A + f(ã1, 72) AA + f(ã2, 71) aa + Mã2, ỹ2) A AA + - (-용) (□)· (-)을• (□)을 • (-꽃)을 Thus we have
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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Transcribed Image Text:Use the Midpoint Rule with m = n = 2 to estimate the value of the integral
IL x - 3y?) da where
EXAMPLE 3
R
2.2)
R
R
SOLUTION In using the Midpoint Rule with m =n= 2, we evaluate f(x, y) = x - 3y2 at the centers of the four subrectangles shown in the figure. So
1, 71 = 5/4, and 2 -
The area of each sub-rectangle is AA =|
Thus
2
« - 3y) da =
-1j-1
Video Example )
- (x1, 71) A + f(ã1, 72) AA + f(ã2, 71) aa + Mã2, ỹ2) A
AA +
- (-용) (□)· (-)을• (□)을 • (-꽃)을
Thus we have
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