Category: Integration

Question Number 174341 by behi834171 last updated on 31/Jul/22 $$1.\underset{1}{\stackrel{2}{\int }}\sqrt{\mathit{x}+\sqrt{\mathit{x}-1}}\mathit{d}\mathit{x}=?$$$$2.\underset{0}{\stackrel{\frac{\mathit{\pi }}{2}}{\int }}\frac{2\mathit{s}\mathit{i}\mathit{n}\mathit{x}+4\mathit{c}\mathit{o}\mathit{s}\mathit{x}}{\mathit{s}\mathit{i}\mathit{n}\mathit{x}+\mathit{c}\mathit{o}\mathit{s}\mathit{x}}\mathit{d}\mathit{x}=?$$ Commented by mnjuly1970 last updated on 30/Jul/22…

Question Number 108789 by 150505R last updated on 19/Aug/20 Answered by 1549442205PVT last updated on 19/Aug/20 $$\mathrm{Choose}\mathrm{A}\mathrm{because}{\int }_{0.5}^1\frac{{\mathrm{x}}^2}{({\mathrm{x}}^2-4)\mathrm{sinx}+\mathrm{x}4\mathrm{cox}}\mathrm{dx}$$$$=\mathrm{ln}\mid\mathrm{cosec}\:\mathrm{2y}+\mathrm{coty}\mid_{\mathrm{0}.\mathrm{5}} ^{\mathrm{1}} =−\mathrm{1}.\mathrm{97}……

Question Number 108761 by bemath last updated on 19/Aug/20 $$\frac{⋮\frac{\mathcal{B}e}{\mathcal{M}ath}⋮}{★}$$$$If{\int }_{-1}^a\frac{x+1}{{(x+2)}^4}=\frac{10}{81},thenthevalueof$$$$a-2is\mathrm{\_}\mathrm{\_}\mathrm{\_}$$ Answered by ajfour last updated on…

Question Number 108748 by john santu last updated on 18/Aug/20 Answered by bemath last updated on 19/Aug/20 $$byparts$$$$\{\begin{array}{l}u=\ln \left(\sin x\right)\Rightarrow du=\frac{\cos x}{\sin x}dx\\ v=\int \sin xdx=-\cos x\end{array}$$$$J=-\cos x\ln \left(\sin x\right)+\int \frac{\cos {}^{2}xdx}{\sin x}$$$${J}=−\mathrm{cos}\:{x}\:\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)+\int\:\frac{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}}…

Question Number 108738 by mnjuly1970 last updated on 19/Aug/20 $$please:{}^{\ast }{\mathrm{prove}}^{\ast }::::$$$$1{.}^{\mathrm{important}}{\lim }_{\mathrm{z}\to 1}(\zeta \left(\mathrm{z}\right)-\frac{1}{\mathrm{z}-1})=\gamma \left(\mathrm{euler}\mathrm{constant}\right)$$$$2.\stackrel{\mathrm{important}}{}{\int }_0^{\mathrm{\infty }}(\cos \left(\mathrm{x}\right)-\frac{1}{1+{\mathrm{x}}^2})\frac{\mathrm{dx}}{\mathrm{x}}=-\gamma$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\mathscr{M}.\mathscr{N}….. \…