iCoachMath.com: Examples on Arc Length and Areas for Parametric Curves - Conics and Parametric Equations, and Polar Coordinates

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f Find the arc length of the polar curve r = e^θ, 0 ≤ θ ≤ 1. f

f Find the arc length of the polar curve r = cos θ, 0 ≤ θ ≤ 2π.
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f Find the arc length of the polar curve r = e^{- θ}, 0 ≤ θ ≤ 1. f

f Determine the arc length of the cardiod r = 1 + cos θ between 0 and π. f

f Find the area of surface formed by revolving the curve r = 1, 0 ≤ θ ≤ π2 about polar axis.
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f Find the area of surface formed by revolving the curve r = sinθ + cosθ, 0 ≤ θ ≤ π2 about the polar axis.
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f Find the arc length of the curve r = sin θ + cos θ, 0 ≤ θ ≤ π4. f

f Find the arc length of the curve r = sec θ, 0 ≤ θ ≤ π3. f

f Find the arc length of the curve r = 1 - cos θ, 0 ≤ θ ≤ π.
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f Find the arc length of the curve r = 1 - sin θ, 0 ≤ θ ≤ π2.
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f Find the area of surface formed by revolving the circle r = 2 cosθ, 0 ≤ θ ≤ π2 about polar axis. f

f Find the area of surface formed by revolving the curve r = sinθ 0 ≤ θ ≤ π2 about the line θ = π2. f

f Find the area of surface formed by revolving the curve r = e^θ, 0 ≤ θ ≤ π4 about the line θ = π2.
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f Find the arc length of the curve r = 1 + sin θ, 0 ≤ θ ≤ π2.
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f Find the arc length of the curve r = 2 from 0 ≤ θ ≤ π2.
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