## Description

I need help in solving 5 questions only in the course calculus 3. For each question solved there has to be the full working out. I'll attach the worksheet here. There 7 questions , but you to answer 5 only

### Unformatted Attachment Preview

MAC 2313 - Calculus III - Exam 4
Name_________________________
Complete the exam on a separate sheet of paper. Solve 5 of the 7 questions below. Each question
is worth 20 points, making the exam worth 100 points. Show all work. Indicate the 5 questions
solved.
1. Evaluate the iterated integral ! ∫∫ ln ( xy ) dA where ! R is the region contained in the rectangle
R
bounded by the lines ! y = 1 , ! y = 3 , ! x = 1 , and ! x = 2 .
2. Evaluate the iterated integral ! ∫
π
0
∫
cos x
0
x dy dx .
3. Evaluate the iterated integral ! ∫∫ y 2 dA where ! D is the region bounded by the functions ! y = x
D
and ! x = y − 2 .
2
4. Evaluate the iterated integral ! ∫
1
5. Evaluate the iterated integral ! ∫
3
∫
0
1
1
3
∫
y
x4 + 1
9−x 2
−3 0
ex
2
dx dy .
+y 2
dy dx .
6. Evaluate the iterated integral ! ∫∫ xy dA where ! D is the region bounded by the circle
D
! x + y = −4y .
2
2
(
)
7. Evaluate the iterated integral ! ∫∫ cos x 2 + 4y 2 dA where ! D is the region bounded by the
D
ellipse ! x 2 + 4y 2 = 1 . (Hint: ! x = 2u and ! y = v .)

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