Compute

We could compute this directly, but to make the computation a bit simpler we use the fact that integrals are invariant under translation (Theorem 1.18 of Apostol). Translating to the left by we have

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Stumbling Robot

A Fraction of a Dot
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Compute an integral of *(2x-5)*^{3}

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Compute

We could compute this directly, but to make the computation a bit simpler we use the fact that integrals are invariant under translation (Theorem 1.18 of Apostol). Translating to the left by we have

Thanks. Got it now. Nice blog by the way.

Hi, I’m also working through Apostol. I don’t see how you used the translation invariance in here.

Hi, I updated the post with some extra details. The translation is to the left by (so the interval of integration moves to the left by that amount) and then we replace with . Of course, cubing that expression and working it out directly should get to the same answer. Let me know if the extra details are clear.