Category: Integration

Question Number 89487 by cindiaulia last updated on 17/Apr/20 $${\int }_{-1}^3\frac{{\mathrm{x}}^2}{\sqrt{\mathrm{x}+2}}\mathrm{dx}$$ Commented by niroj last updated on 17/Apr/20 $$\:\int_{−\mathrm{1}} ^{\:\mathrm{3}} \:\frac{\:\mathrm{x}^{\mathrm{2}}…

Question Number 155016 by ArielVyny last updated on 24/Sep/21 $${\int }_0^{\mathrm{\infty }}{tan}^{2}u(1-\frac{1}{{(u+1)}^2})du$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 154928 by qaz last updated on 23/Sep/21 $$\mathrm{Prove}::\underset{\mathrm{k}=0}{\sum ^{\mathrm{m}}}{\left(\begin{array}{c}\mathrm{m}\\ \mathrm{k}\end{array}\right)}^2\left(\begin{array}{c}\mathrm{n}+2\mathrm{m}-\mathrm{k}\\ 2\mathrm{m}\end{array}\right)={\left(\begin{array}{c}\mathrm{m}+\mathrm{n}\\ \mathrm{n}\end{array}\right)}^2$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 154926 by physicstutes last updated on 23/Sep/21 $${\int }_0^1\frac{2x^2}{{(x^2+1)}^2}dx=$$ Answered by qaz last updated on 23/Sep/21 $$\int_{\mathrm{0}}…

Question Number 89384 by nimnim last updated on 17/Apr/20 Commented by mathmax by abdo last updated on 17/Apr/20 $$lettryanotherwayweconsiderthediffeomorphism$$$$(u,v)\to (x,y)/x-y=uandx+y=v\Rightarrow x=\frac{u+v}{2}andy=\frac{-u+v}{2}$$$$\Rightarrow\varphi\left({u},{v}\right)=\left(\varphi_{\mathrm{1}} \left({u},{v}\right),\varphi_{\mathrm{2}} \left({u},{v}\right)\right)=\left({x},{y}\right)=\left(\frac{{u}}{\mathrm{2}}+\frac{{v}}{\mathrm{2}},−\frac{{u}}{\mathrm{2}}+\frac{{v}}{\mathrm{2}}\right)…