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Results tagged with integration
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user 9833
Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...
1
vote
Bounding an elliptic-type integral
After $x=Kt^{2/3}$, using an obvious inequality $\sqrt{A+B}\le\sqrt{A}+\sqrt{B}$,
we have
$$\int_0^L \sqrt{x\left(1+\frac{1}{K-x}\right)}\,dx\le \frac{2}{3}L^{3/2}+K\int_0^{L/K}\sqrt{\frac{t}{1-t}}\,d …
- 6,891
2
votes
Quadrature formula max accuracy
As Federico Poloni said, it is a special case of Gauss-Jacobi quadrature.
I am in a good mood, so here is your homework. The formula is
$$\int_{-1}^{1}\sqrt{\frac{1-x}{1+x}}f(x)dx=
\frac{\pi(5+\sqrt{ …
- 6,891