MAC 2313 Iterated Integral and Region Bound Calculus 3 Exam 4 Answers

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MAC 2313

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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

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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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