# Evaluate the path integral $\int_{γ_1}(Re\:z)^2dz$

Evaluate the path integral: $$\int_{γ_1}(Re\:z)^2dz$$ where $γ_1 = [z_0, z_1]$ (the straight-line path connecting $z_0$ and $z_1.$)

I'm really not sure how to approach this question so any help will be appreciated.

• Did you try parameterizing the curve? – Fabian Mar 14 '17 at 18:36

Parametrize as $\gamma_1= tz_0 + (1-t) z_1,\; t \in [0,1]$ and convert to $$(z_0 -z_1)\int_0^1 \left( t\Re z_0 + (1-t) \Re z_1 \right)^2 \; \mathrm{d} t$$