9. Consider the volume of the solid region lying

below the surface z=f(x,y) and above the

plane region R.

f(x) = (x+y)

R: the region of the xy-coordinate plane

bounded by the square with vertices (4,0),

(6,2), (4.4), and (2.2)

a) Sketch the region R and calculate its area.

6

5

4

3

2

1

0

0)

c) Sketch the region S and calculate its area.

6

5

4

0 1 2 3 4 5 6

b) Define the transform you will be using to evaluate the integral. (T or T¹ will be acceptable)

2

1

0

400-

200

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d) How much larger is the area of your simpler gion 5 than the Region R7

200-

f) Calculate the volume.

Consider the integral [ f(x, y)dyde and the equivalent integral [ 90.)

Based on your transformation, determine the appropriate Jacobian (x,y)

2(x)

(u, v)

dudv.