WorkingPrecision is an option for various numerical operations which specifies how many digits of precision should be maintained in internal computations.
WorkingPrecision is an option for such functions as NIntegrate and FindRoot.
n causes all internal computations to be done to at most n-digit precision.
Even if internal computations are done to n-digit precision, the final results you get may have much lower precision.
See the Mathematica book: Section 3.9.3, Section 3.9.3.
See also: AccuracyGoal, Precision, Accuracy, N.
This evaluates the integral using 40-digit precision for internal computations. The precision goal in this case is automatically set to 30 digits.
The difference from the exact result is given as a number close to 0.
In fact, the result was correct to about 33 digits.
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