HW13-solutions rusin

# 4 3y dxdy when a is the region 1 i 100

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Unformatted text preview: x − 4) − 3y } dy dx. Now Explanation: After integration with respect to y we see that 1 5 3xy − y 2 2 I= 0 1 = 0 = x2 0 {4(x − 4) − 3y } dy 0 dx = 5 3 x3 − x4 d x 2 34 15 x− x 4 2 x −4 0 . x −4 0 . Consequently 6 1 3 4(x − 4)y − y 2 2 I= 4 5 (x − 4)2 dx = 2 5 (x − 4)3 6 6 4 , rogers (grr459) – HW13 – rusin – (55220) 6 y and so I= 011 20 3 4 . 10.0 points Reverse the order of integration in the integral x 2x 2 2 f (x, y ) dy dx , I= 0 0 but make no attempt to evaluate either integral. 2 4 1. I = f (x, y ) dx dy y 0 Integration is taken ﬁrst with respect to y for ﬁxed x along the dashed vertical line. To change the order of integration, now ﬁx y and let x vary along the solid horizontal line in y y 4 2. I = f (x, y ) dx dy 0 4 2 4 2 3. I = f (x, y ) dx dy correct y/2 0 2y 2 4. I = f (x, y ) dx dy 0 0 y /2 4 5. I = x f (x, y ) dx dy 0 2 4 6. I = f (x, y ) dx dy 0 2 0 2y Explanation: The region of integration is the set of all points (x, y ) : 0 ≤ y ≤ 2x , 0 ≤ x ≤ 2 in the plane bounded by the x-axis and the graphs of y = 2x , x = 2. This is the shaded region in Since the equation of the slant line is x = y/2, integration in x is along the line from (y/2, y ) to (2, y ) for ﬁxed y , and then from y = 0 to y = 4. Consequently, after changing the order of integration, 4 2 I= f (x, y ) dx dy 0 . y/2 keywords: double integral, reverse order integration, linear function,...
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## This note was uploaded on 09/22/2013 for the course M 408 D taught by Professor Textbookanswers during the Fall '07 term at University of Texas.

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