Complex Analysis: Theory and Applications · Problem 6.1.5

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-integral-product

Problem

Let

f(t) = u(t) + iv(t)

, where

u

and

v

are differentiable. Show that

\int_a^b f(t)f'(t)\,dt = \frac{1}{2}[f(b)]^2 - \frac{1}{2}[f(a)]^2.