(5) a) Sketch r = 3+ 3 cosθ and b) Find the are length of the curve for 2π/3 ≤ θ ≤ π
As you've asked to solve the part (b), therefore, I'm solving that part.
Solution: The arc length of a polar curve r = f(θ) between θ = a and θ = b is given by the integral:
(1)
Given the curve:
(2)
Differentiating this equation w.r.t , we'll get:
(3)
Since we've to calculate the length of the polar between,
(4)
in equation (1). Thus, we've to calculate,
Using (1), (2), (3) and (4), we'll get:
On simplifying, we'll get:
Now solving,
Rewriting using trigonometric identity,
We'll get:
On integration, we'll get:
Therefore,
Substituting limits, we'll get:
I hope it helps you!
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