I have another question (studying for finals, haha)

Question

Let ~r(t) = et cost
~i + et sin t~j be parametric equations of a curve C. Find the length of
C from t = 0 to t = π.

so the equation I am using is the integral from a to b (in thsi case 0 to pi) of the magnitude of r'(t) dt

I get 0 because I get 2e^tsint as my integrated magnitude and when sint is 0 or pi it is just 0.

but the answer is sqrt(2) (e^pi -1)

Answer 1

ok so now i get that i did the integral wrong,. it should be 2e^t(sint+cost) but I get 2(e^pi -1) for sqrt2??