OldFinalb.pdf - Math 172 Second Semester Calculus Fall...

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Math 172: Second Semester Calculus Fall Semester, 2016 Final Exam Name: Section: Work must be shown to receive credit. No calculators. sin𝜋𝜋3=32cos𝜋𝜋3= 1/2sin𝜋𝜋4=22cos𝜋𝜋4=22sin𝜋𝜋6=12cos𝜋𝜋6=12sin2(𝑥𝑥) =12(1cos(2𝑥𝑥)) cos2(𝑥𝑥) =12(1 + cos(2𝑥𝑥))# 1 2 3 4 5 6 subtotal worth 13 12 13 13 12 13 76 # 7 8 9 10 11 12 subtotal total worth 12 12 12 13 12 13 74 150
Question 1 (13 points)Find the area bounded by the parabola 𝑦𝑦=𝑥𝑥2and the line 𝑦𝑦=𝑥𝑥2.
Question 2. (12 points)Find the volume of the solid of revolution generated by rotating the following region about the 𝑥𝑥-axis: the region bounded by 𝑦𝑦= sin(𝑥𝑥)and 𝑦𝑦= 0on the interval [0,𝜋𝜋].
Question 3 Evaluate the following indefinite integrals. a. (7 points)
3
b. (6 points)
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