Compute an integral of (x+1)^2

by RoRi

July 23, 2015

Compute:

$\int_{-1}^0 (x+1)^2 \, dx.$

Here, we use the fact that the integral is invariant under translation (Theorem 1.18 of Apostol),

$\int_{-1}^0 (x+1)^2 \, dx = \int_{-1+1}^{0+1} (x-1+1)^2 \, dx = \int_0^1 x^2 \, dx = \left. \frac{x^3}{3} \right|_0^1 = \frac{1}{3}.$

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