Compute the integral from x to x^2 of (t^2 + sin t)

by RoRi

August 4, 2015

Compute the following integral

$\int_x^{x^2} (t^2 + \sin t) \, dt.$

The computation is as follows:

$\begin{align*} \int_x^{x^2} (t^2 + \sin t) \, dt &= \left. \frac{t^3}{3} \right|_x^{x^2} - \cos t \biggr \rvert_x^{x^2} \\ &= \frac{x^6}{3} - \frac{x^3}{3} - \cos (x^2) + \cos x. \end{align*}$

Stumbling Robot

Compute the integral from x to x^2 of (t^2 + sin t)

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