$$A=\displaystyle \lim_{ n\to \infty}\sum_{i=1}^{n}f(x_{i})\Delta x$$ $$where: \Delta x=\frac{b-a}{n}$$

$$\sum_{i=1}^{n}1=n$$ $$\sum_{i=1}^{n}i=\frac{n(n+1)}{2}$$ $$\sum_{i=1}^{n}i^2=\frac{n(n+1)(2n+1)}{6}$$ $$\sum_{i=1}^{n}i^3=\left [ \frac{n(n+1)}{2} \right ]^2$$

$$\frac{\mathrm{d} }{\mathrm{d} x}\sin x=\cos x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cos x=-\sin x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\tan x=\sec^2x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\csc x=-\csc x\cot x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\sec x=\sec x\tan x$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cot x=-\csc^2x$$

$$\frac{\mathrm{d} }{\mathrm{d} x}\sin^{-1}x=\frac{1}{\sqrt{1-x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cos^{-1}x=-\frac{1}{\sqrt{1-x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\tan^{-1}x=\frac{1}{{1+x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\cot^{-1}x=-\frac{1}{{1+x^2}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\sec^{-1}x=\frac{1}{x\sqrt{x^2-1}}$$ $$\frac{\mathrm{d} }{\mathrm{d} x}\csc^{-1}x=-\frac{1}{x\sqrt{x^2-1}}$$

$$\int_{}^{}udv=uv-\int_{}^{}vdu$$