Category: Integration

Question Number 65771 by mathmax by abdo last updated on 03/Aug/19 $$let{X}_n={\int }_0^{\frac{\pi }{4}}{sin}^{n}xdx$$$$1)calculate{X}_0,X_1,X_2,X_3$$$$\left.\mathrm{2}\right)\:{find}\:{X}_{{n}} {interms}\:{of}\:{n} \…

Question Number 65763 by 9325328488 last updated on 03/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 216 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}$$$$\underset{-\mathrm{\infty }}{\stackrel{+\mathrm{\infty }}{\int }}f\left(x\right)dx$$$$\mathrm{where}$$$$f\left(x\right)=\{\begin{array}{ll}{e}^x& x⩽0\\ 1+x& 0<x⩽1\\ 1+x^2& 1<x⩽2\\ 5& 2<x⩽5\\ \frac{5}{1+{(x-5)}^2}& x>5\end{array}$$ Answered by…

Question Number 65740 by rajesh4661kumar@gmail.com last updated on 03/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $$letA=\int \frac{dx}{\frac{1}{cosx}+sinx}\Rightarrow A=\int \frac{cosx}{1+cosxsinx}dxchangement$$$${tan}\left(\frac{{x}}{\mathrm{2}\:}\right)\:={t}\:{give}\:{A}\:=\int\:\:\:\frac{\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{1}+\frac{\mathrm{2}{t}\left(\mathrm{1}−{t}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}}…

Question Number 191 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\underset{\mathrm{C}}{\int }\frac{z^2\sin z\cos z}{(z^2+1)(z^2-1)}dz$$$$\mathrm{where}\mathrm{C}=\{z\in \mathbb{C}\mid \mid z\mid =2\}$$ Answered by nileshkulkarni last updated on 15/Dec/14…