1. Use the given transformation to evaluate the integral.

(10x + 15y) dAR

,

where R is the parallelogram with vertices (?2, 8),

(2, ?8),

(5, ?5),

and (1, 11)

; x =1

5

(u + v), y =1

5

(v ? 4u)

Evaluate the integral by making an appropriate change of variables.

7(x + y) e^{x2 ? y2}dA,R

where R is the rectangle enclosed by the lines x ? y = 0,

x ? y = 4,

x + y = 0,

and x + y = 7

TAKE HOME EXAM Answer all questions carefully , showing all work on a separate paper to receive full credit Compute the integral REX R 52 + y with the parallelogram enclos ed by the lines 20 - 32 - 0 , 2 2 - By = 2 S ty = 1 and SIty = 3 16ed with the region bounded by the ellipse 9 2 2 + 4 2 = 36 1 1 2 + Bee Rag with R the rectangle enclosed by a - y = 0 , 2 - y = 2 , 2 + y = 0 and Ity = 3 2 . Find the Jacobian of the transformation 2 2 = 4 4 120 , y = 6 + WEL , 2 = 20 + 20 b . = = pes , y = gep 3 . Compute the integral Soydoc + ady + Idz , where to ( 2 0 4 ) foll consists of CI , the line segment from ( 3 , 1 , 2 ) ( 1 , - 1 , 1 ) to ( 2 0 4 ) followed by C2 , the line segment from ( 2 0 4 ) to Soyds where C is the curve I = 1 2 , y = 21 0