Trigonometric Integrals Trigonometric Substitutions

6.1 Integration by Parts 6.1 Exercises 6.2 Trigonometric Integrals and Substitutions Trigonometric Integrals Trigonometric Substitutions 6.2 Exercises 6.3 Partial Fractions 6.3 Exercises 6.5 Approximate Integration Simpson’s Rule 6.5 Exercises 6.6 Improper Integrals Type 1: Infinite Intervals Type 2: Discontinuous Integrands A Comparison Test for Improper Integrals PROBLEM 1 (4 pts) 2 (4 pts) 3 (4 pts) 4 (5 pts) 5 (5 pts) 6 (4 pts) 7 (4 pts) TOTAL (30 pts) SCORE Solve all problems below. Duration: 50 min. Be neat, show your work to receive credit. 1 1 (4 points) (a) Does 669 dt converge? Why? Hint: Let x = e. et + e- w – 2 – COS X (b) Does dx converge? Why? х (4 points) Evaluate | 2x 는 2x – 3 dx. x2 W 3 pr/4 (4 points) Evaluate 6.** tan4(x) dx. 4 (5 points) Evaluate Lovingade. ho 1 5 (5 points) Evaluate -1 sin dx. Hint: First, set y = x 6 (4 points) Using S8 (Simpson’s Rule with n = 8) estimate Live x² dx. 7 (4 points) Find the smallest n guaranteeing that Simpson’s rule Sn for x In x dx is accurate to within 5 x 10-4.
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