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# Integrals and Average Sums

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keywords: integration, integrates, integrals, integrating, double, triple, multiple

20. The average sum is used to approximate

to the indicated accuracy. How large must n be chosen for this to be true?

Could someone please tell me what am I doing wrong here. Thank you

##### Solution Summary

Integrals and average sums are investigated.

##### Solution Preview

Dear Student,

The problem is that you are trying to calculate the integral explicitly. This cannot be done. All you can do is evaluate it numerically, using for example the Average Sum numerical integration method. To do this you split up the integration interval [0,3] into N small parts, [0,3/N],[3/N,3/N *2] etc. The integration is approximated by taking e^(x^2) to be approximately constant in each of these small parts (which is certainly true for large enough N). Then the integral is equal to the sum over all little ...

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