User:Superdan006/Sandbox/hw2

$\int _{0}^{1}{\frac {4}{1+x^{2}}}\,dx\$

$\int _{a}^{b}f(x)\,dx\approx {\frac {b-a}{2n}}\sum _{i=0}^{n-1}[f_{i}+f_{i+1}]$

$R(n,m)=R(n,m-1)+{\frac {1}{4^{m}-1}}[R(n,m-1)-R(n-1,m-1)]$

$\int _{a}^{b}f(x)\,dx\approx \sum _{i}\omega _{i}f(x_{i})$

$\int _{0}^{2\pi }{\frac {\cos {2x}}{e^{x}}}\,dx\$

$\int _{a}^{b}f(x)\,dx\approx {\frac {(b-a)}{6}}\left[f(a)+4f\left({\frac {a+b}{2}}\right)+f(b)\right]$.

$\int _{0}^{1}{\frac {\cos {x}}{\sqrt {x}}}\,dx$

${\begin{aligned}\int _{0}^{1}{\frac {\cos {x}}{\sqrt {x}}}\,dx&{}=\int _{0}^{1}{\frac {\cos {u^{2}}}{u}}(2u)\,du\\&{}=\int _{0}^{1}\cos {u^{2}}\,du\end{aligned}}$