sum7.1.21 - Week 2 Homework Wed Thurs Mon 3.6 Implicit...

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Unformatted text preview: Week 2 Homework: Wed, Thurs, Mon 3.6 Implicit diff #49 3.8 Log derivatives #4 5.5 Integration by substitution continued Text Ex 2, #26 2 6.1 areas #19, #9 (today) 6.2 volumes: disks, washers Text #2, #6, 26, 28 7.1 integration by parts #6, text #3, #10 (like text #5), #15 (like text #4), #21 see below 7.2 trig integrals #2, #14 see below, 26, text #8 7.3 trig substitution text ex 1, 3 Problem 7.1.21: 2 Evaluate 1 ln x dx. 2 x Solution: This problem resembles Text example 2, which used u = ln x for ln x dx. (read/recall!) dx x , Taking u = ln x again, du = ln x dx = 2 x = -x-1 ln x + = -x-1 ln x - x-2 dx, 1 + c, x 1 where dv = x-2 dx gives v = - x . 2 So 1 ln x dx 2 x = [-x = 1 2 -1 1 2 1 2 ln x - ]1 x ln 2. - 4 Problem 7.2.14: Evaluate 0 2 sin2 x cos2 x dx. Solution: (Sketch.) Both exponents are even, so we use the double angle formula (for both cos2 and sin2 ). We get an integral in cos2 (2x), and use the double angle formula again. ...
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sum7.1.21 - Week 2 Homework Wed Thurs Mon 3.6 Implicit...

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