Category: Integration

Question Number 212626 by Ghisom last updated on 19/Oct/24 $$\mathrm{let}f\left(x\right)=\frac{1}{\sqrt{(x-a)(x-b)(x-c)}}$$$$\mathrm{let}a,b,c\in \mathbb{R}\wedge a<b<c$$$$\Rightarrow D\left(f\left(x\right)\right)=(a,b)\cup (c,\mathrm{\infty })$$$$\mathrm{prove}\underset{a}{\stackrel{b}{\int }}f\left(x\right)dx=\underset{c}{\stackrel{\mathrm{\infty }}{\int }}f\left(x\right)dx$$ Answered by MrGaster…

Question Number 212319 by Ghisom last updated on 09/Oct/24 $$\mathrm{find}$$$$G=\frac{1}{4}\underset{0}{\stackrel{\pi /2}{\int }}\ln \frac{1+\sin x}{1-\sin x}dx$$ Commented by Spillover last updated on 10/Oct/24 $$\frac{\pi}{\mathrm{4}}\mathrm{ln}\:\mathrm{2}\:\:{right}? \…

Question Number 212139 by mnjuly1970 last updated on 03/Oct/24 $$$$$$$$$$$$$${\mathrm{I}}_n={\int }_{-\pi }^{\pi }\frac{\sin \left(nx\right)}{(1+e^x)\sin x}dx=?$$$$$$ Answered…

Question Number 212053 by universe last updated on 28/Sep/24 $$$$$$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\int_{\mathrm{0}} ^{\:\boldsymbol{{y}}} \:\boldsymbol{{e}}^{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} } \boldsymbol{{dx}}\right)\boldsymbol{{dy}}\:+\int_{\mathrm{1}} ^{\mathrm{2}} \left(\int_{\mathrm{0}} ^{\:\mathrm{2}−\boldsymbol{{y}}} \:\boldsymbol{{e}}^{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }…

Question Number 211995 by SVMEHTA last updated on 26/Sep/24 $$\int \sqrt{}tanxdx$$ Commented by Frix last updated on 26/Sep/24 $$\mathrm{Use}t=\sqrt{\tan x}$$ Commented by BHOOPENDRA…