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Monte Carlo Integration - function np.sin(θ)^24) / (θ^2) where 0<θ<∞ .

How can we integrate this function over a bounded domain and get an accurate result and what bounds should you choose to get a result within 0.001 of the correct solution?

All help welcome.

mikemerrill
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  • Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments. – José Carlos Santos Sep 21 '18 at 06:32

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One option: Find $g$ such that $$\int_0^\infty f(x)\,\mathrm dx = \int_0^1 g(x)\,\mathrm dx.$$

But I suppose, you are expected to find $h$ such that $|f(x)|\le h(x)$ and $H(a):=\int_a^\infty h(x)\,\mathrm dx$ is easily computed formally. Then find $a$ to make $H(a)<\frac12\epsilon$ and compute $\int_0^af(x)\,\mathrm dx$ numerically with an expected error $<\frac12\epsilon$ as well.

Hagen von Eitzen
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