Compute the integral of (sin t, cos t, tan t)

by RoRi

May 31, 2016

Compute the vector-valued integral

$\int_0^{\frac{\pi}{4}} (\sin t, \cos t, \tan t) \, dt.$

We compute

$\begin{align*} \int_0^{\frac{\pi}{4}} (\sin t, \cos t, \tan t) \, dt &= \left( \int_0^{\frac{\pi}{4}} \sin t \, dt, \int_0^{\frac{\pi}{4}} \cos t \, dt, \int_0^{\frac{\pi}{4}} \tan t \, dt \right) \\[9pt] &= \left( 1 - \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}, - \log \frac{\sqrt{2}}{2} \right). \end{align*}$

Stumbling Robot

Compute the integral of (sin t, cos t, tan t)

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