What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (15 points)

Question

What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (15 points) 
A) 8
B) 4 times the square root of 2
C) 4
D) 8 times the square root of 2

oobleck · Accepted Answer

I got 4√2

oobleck · Answer

s = ∫[0,π] √((dx/dt)^2 + (dy/dt)^2) dt
= ∫[0,π] √((1+sint)^2 + (cost)^2) dt
= ∫[0,π] √(1+2sint+sin^2t + cos^2t) dt
= ∫[0,π] √(2+2sint) dt
Now you can use your sum-to product formulas to get the job done.

Jackie · Answer

I got 4, can you check this? Please!