Math 237
Assignment 11 Solutions
0
1. Use T (x, y ) = (x + y, x + y ) to evaluate
y
(x
0
+ y ) cos(x y ) dx dy .
Solution: We have u = x + y and v = x + y . The region of integration is 0 x y
and 0 y . Thus, the region is bounded by the lines x = 0, y =
Math 237
Assignment 9 Solution
1. Invent an invertible transformation that transforms the ellipse 3x2 + 6xy + 4y 2 = 4 onto the unit circle and determine the inverse map. Solution: Completing the square we get 3 x2 + ( 3 x + 2y)2 = 4. Dividing by 4 gives
Math 237
Assignment 10 Solutions
1. Find the volume of the solid with height h(x, y) = 1+xy and base D where D is bounded by y = x and y = x2 . Solution: Sketching the region we get the region to the right Drawing rectangles vertically we get Hence
1
x2 y