Question

Evaluate integral of 2+x^2y ds where C is the upper half of x2 + y2 = 1 using the following naive parametrization for C: r(t)=, -1= 13 years ago

Answer 1

this is a linear integral by the way

Answer 2

x = cost, y = sint, 0 <= t <= pi

∫(2 + cos²t sint) √( (-sint)² + cos²t) dt
∫(2)dt + ∫cos²t sint dt
= 2/3 + 2pi