HW13-solutions rusin

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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,...
View Full Document

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.

Ask a homework question - tutors are online