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Calculus
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13 Nov 2019

Consider the curve with polar equation r = θ, 0 ≤ θ ≤ 2π.

1)Sketch the curve.

2)Write, but do not evaluate, an integral that represents the length of the curve.

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Tod Thiel
Tod ThielLv2
26 Sep 2019

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Related questions

Answer all 3 parts please. Thank you.
1. Graph the directed curve r = sin(3θ) for 0 ≤ θ ≤ 2π . Include arrows on the curve to indicate the path taken as θ increases (from 0 to 2π).
Number/label each petal for θ starting at 0 and increasing to 2π.
2. Provide the table for r = sin(3θ) for 0 ≤ θ ≤ 2π. For θ to go from 0 to 2π, you will need to list below SIX petals with SIX corresponding intervals for θ (See the table in the picture).
3. Use integration with respect to polar coordinates to compute the area of one petal of the curve r = sin(3θ).


Express the length L of the curve r = sin3(θ), 0 ≤ θ ≤ pi/2 as an integral but do not evaluate it.

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x = 4 sin2(t), y = 4 cos2(t), 0 ≤ t ≤ 2π

What is the length of the curve?

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Consider the function r = 2 cos(θ) + sin(2θ).

By looking at the Cartesian graph, where is r ≤ 0? (For 0 ≤ θ ≤ 2π. Enter your answer using interval notation.)

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