what's the arc length of an ellipse?

Question

I need to find the arc lenght of an ellipse:
x^2/(a^2) + y^2/(b^2) = 1

using parametric equations and the formula
L = ∫sqrt( (dx/dt)^2 + (dy/dt)^2)dt
x= a sin θ
y= b cos θ
θ = [0,2π]

Answer 1

Here is a short cut: Arc length = pi*a*b (where a is the semi-major radius and b is the semi-minor radius).

Answer 2

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