MATH111-200630-ST02

MATH111-200630-ST02 - 3. Evaluate the following integral: x...

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UNIVERSITY OF REGINA DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 111–002 200630 Sample Midterm Test 2 Time: 50 minutes Name: Instructor: Student #: Dr. Edward Doolittle Section: You have 50 minutes to do each of the following questions. Please check your work carefully. The test is worth a total of 50 marks. Non-programmable calculators, logarithm tables, and/or slide rules are permitted; no other aids are permitted. Use the backs of the pages for rough work. 1. (10 marks) Find the following integral: x 2 e x dx . 2. (10 marks) Find the following trigonometric integral: π 2 0 sin 5 x dx . Page 1 of 4
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MATH 111–002 200630 Midterm Test 2 Page 2 of 4 Time: 50 minutes Name: Student #: Section:
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Unformatted text preview: 3. Evaluate the following integral: x 9 x 5 x 2 dx . MATH 111002 200630 Midterm Test 2 Page 3 of 4 Time: 50 minutes Name: Student #: Section: 4. (10 marks) Evaluate the integral 5 4 x x 2 dx . You may find some of the formulas tan d ln sec C sec d ln sec tan C sec 3 d 1 2 sec tan 1 2 ln sec tan C helpful. MATH 111002 200630 Midterm Test 2 Page 4 of 4 Time: 50 minutes Name: Student #: Section: 5. (10 marks) (a) Prove the reduction formula sin n x dx 1 n cos x sin n 1 x n 1 n sin n 2 x dx (b) Show that, for odd powers 2 n 1 of sine, 2 sin 2 n 1 x dx 2 4 6 2 n 3 5 7 2 n 1 ....
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MATH111-200630-ST02 - 3. Evaluate the following integral: x...

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