Home » Blog » Compute the integral of (sin t, cos t, tan t) Compute the integral of (sin t, cos t, tan t) by RoRi May 31, 2016 Compute the vector-valued integral We compute Related
July 19, 2023 at 1:01 am S says: I got the same like here, minus sign is lacking in the 3rd dimension in the book.
![\[ \int_0^{\frac{\pi}{4}} (\sin t, \cos t, \tan t) \, dt. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-d5da456b9051f53d8d5ea05a70af28d3_l3.png "Rendered by QuickLaTeX.com")
![\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*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-e21f37861f9623e46c53958785daf644_l3.png "Rendered by QuickLaTeX.com")
I got the same like here, minus sign is lacking in the 3rd dimension in the book.