fall17mth143.practice2.11-PolarCalc.pdf

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Length = Answer(s) submitted: (incorrect) Correct Answers: 4 9. (1 point) Find the exact length of the polar curve r = 3sin ( θ ) , 0 θ π / 3 . Length = Answer(s) submitted: (incorrect) Correct Answers: 3

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pi 10. (1 point) Find the arc length of the polar curve described by: r = 6 + 6cos θ Answer(s) submitted: (incorrect) Correct Answers: 48 11. (1 point) Find the length of the spiral r = θ for 0 θ 5. Answer : Solution: Solution: We use the formula for the arc length. In this case f ( θ ) = θ , f 0 ( θ ) = 1. Using integration formulas we get: S = Z 5 0 p θ 2 + 1 2 d θ = Z 5 0 p θ 2 + 1 d θ = θ 2 p θ 2 + 1 + 1 2 ln | θ + p θ 2 + 1 | 5 0 = 5 2 p 5 2 + 1 + 1 2 ln | 5 + p 5 2 + 1 | ≈ 13 . 904 Answer(s) submitted: (incorrect) Correct Answers: 13.9038 Generated by c WeBWorK, , Mathematical Association of America 4
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