Home > Calculus > Determining the Length of a Polar Curve

How do you find the length of a petal of a polar curve?

Answer 1

Evelyn Agard

The Arc Length in Polar Coordinates is given bu:

# L = int \ dS # where # dS=sqrt(r^2+((dr)/(d theta))^2) \ d theta #

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Answer 2

Paisley Johnson

To find the length of a petal of a polar curve, you can use the following formula:

Length of a petal = ∫[θ1 to θ2] √[r(θ)^2 + (dr/dθ)^2] dθ

where r(θ) is the polar function representing the curve, and θ1 and θ2 are the angles defining the petal. You integrate this expression over the given range of θ values to find the length of the petal.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.