Complex Analysis: Theory and Applications · Problem 6.1.1

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-integrals-real-variable

Problem

Use Equations (6.1) and (6.2) to find (a)

\displaystyle\int_0^1 (3t-i)^2\,dt

. (b)

\displaystyle\int_0^1 (t+2i)^3\,dt

. (c)

\displaystyle\int_0^{\frac{\pi}{2}} \cosh(it)\,dt

. (d)

\displaystyle\int_0^2 \frac{t}{t+i}\,dt

. (e)

\displaystyle\int_0^{\frac{\pi}{4}} t\exp(it)\,dt