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.