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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.8 Numerical Integration, #23 · Calculus · Integrals

The graph of … has a sharp spike and a long tail

The graph of $y (x) = 1/ (x^{2} + 1 0^{- 10})$ has a sharp spike and a long tail. Estimate $\int_{0}^{1} y d x$ from $T_{10}$ and $T_{100}$ (don't expect much). Then substitute $x = 1 0^{- 5} tan θ$ , $d x = 1 0^{- 5} sec^{2} θ d θ$ and integrate $1 0^{5}$ from 0 to $π /4$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.8 Numerical Integration, #23

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