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Find the exact length of the polar curve r = 2, 0 ≤ θ ≤ 5/4.

User Tom Damon
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Final answer:

The exact length of the polar curve r = 2, 0 ≤ θ ≤ 5/4 is 5/2.

Step-by-step explanation:

The polar curve is given by r = 2. To find the exact length of the curve, we need to integrate the arc length formula. The arc length formula in polar coordinates is given by:

s = ∫√(r^2 + (dr/dθ)^2)dθ

Since r = 2 and dr/dθ = 0 (since r is constant), the integral simplifies to:

s = ∫2dθ

Integrating both sides gives:

s = 2θ

Plugging in the limits of integration 0 ≤ θ ≤ 5/4, we get:

s = 2(5/4) - 2(0) = 5/2

Therefore, the exact length of the polar curve r = 2 for the given range of θ is 5/2.

User Nava
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