Using L'Hopitals rule for evaluating indeterminate forms, just differentiate both the numerator and the denominator separately to produce 1/1. Xyius explains well intuitively why the result is what it is.
Homework Statement
Find the length of the polar curve.
Complete the cardioid r=1+cosθ
Homework Equations
L=∫αβ√[f(θ)2+f'(θ)2] dθ
The Attempt at a Solution
Given f(θ)2 is equal to cos2θ+2cosθ+1
and f'(θ)2=sin2θ
I arrive at the integral ∫αβ√[2cosθ+2] dθ which I cannot for the life of me...