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if f(x) approximate g(x) within 1/3000 for 10

Mathematics
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you always come up with the damndest questions but lets say \(f(x)=0\) and \(g(x)=\frac{1}{3000}\) which is as far as it can be then \[\int_{10}^{12}f(x)dx=0\] and \[\int_{10}^{12}\frac{1}{3000}=\frac{2}{3000}\]
a more sophisticated way to answer would be to say that \[\int f -\int g =\int (f-g)\leq \int \frac{1}{3000}=\frac{2}{3000}\]
an even more sophisticated way to answer would be to use absolute values, but enough already

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