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Re: Math Quiz 9
Precisely ln(1+sqrt(2))/3 + sqrt(2)/15 + 2/15
Or approximately 0.52140543316
Rounded to 8 digits: 0.52140543
Rounded to 5 digits: 0.52141
A fun exercise in every integration tool I've ever learned, plus a cool rationalization trick I wasn't familiar with.
The computation took a bit to hash through some arithmetic errors and one silly differential error (chain rule!). In practice you probably wouldn't bother to do this (or use a symbolic manipulation tool like Mathematica - this is how I checked my work), and sometimes there is no closed form for the integral. To get 8 digits simply run a larger Monte Carlo simulation (a couple lines of code instead of several pages of derivation). In the end we are always limited to some finite number of digits, so numerical methods win out.
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