Compute the integral

by RoRi

August 20, 2015

Compute the following integral:

$\int_0^{2y} (1 + t + t^2) \, dt.$

We have

$\int_0^{2y} (1+t + t^2) \, dt = \left. \left( t + \frac{t^2}{2} + \frac{t^3}{3} \right) \right|_0^{2y} = 2y + 2y^2 + \frac{8}{3} y^3.$

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