Compute the integral

by RoRi

August 22, 2015

Compute the following integral:

$\int_x^{x^2} (v^2 + \sin 3v) \, dv.$

We have

$\begin{align*} \int_x^{x^2} (v^2 + \sin 3v) \, dv &= \int_x^{x^2} v^2 \, dv + \int_x^{x^2} \sin 3v \, dv \\ &= \left(\frac{x^6}{3} - \frac{x^3}{3} \right) + \frac{1}{3} \int_{3x}^{3x^2} \sin v \, dv \\ &= \frac{1}{3} \left( x^6 - x^3 + \cos 3x - \cos (3x)^2 \right). \end{align*}$

One comment

May 29, 2020 at 12:20 am

Mihajlo says:

cos((3x)^2) should be cos(3(x^2)).

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Stumbling Robot

Compute the integral

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