Compute the following integral
![\[ \int_0^{\pi/2} \sin 2x \, dx. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-eeb526a1b94cddbe32b03a8ae293d590_l3.png "Rendered by QuickLaTeX.com")
Later we will have some more options on how to do this, but for now we use the expansion/contraction of the interval of integration (Theorem 1.19 from Apostol) and compute,
![\[ \int_0^{\frac{\pi}{2}} \sin (2x) \, dx = \frac{1}{2} \int_0^{\pi} \sin x \, dx = \frac{1}{2} (1 - \cos \pi) = 1. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-d196691ad0e6a0055434f4c0baf5a087_l3.png "Rendered by QuickLaTeX.com")
Compute the following integral
Later we will have some more options on how to do this, but for now we use the expansion/contraction of the interval of integration (Theorem 1.19 from Apostol) and compute,