Category: Integration

Question Number 141 by shahid.ansari56@yahoo.com last updated on 25/Jan/15 $$56546557\mathbf{÷}vb65$$$$$$ Answered by 123456 last updated on 14/Dec/14 $$\frac{56546557}{65vb},vb\ne 0$$ Terms…

Question Number 131211 by mnjuly1970 last updated on 02/Feb/21 $$\dots calculus\dots$$$$provethat::$$$$\mathbf{\Phi }={\int }_0^{\frac{\mathit{\pi }}{4}}\left(\frac{\sqrt{\mathit{t}\mathit{a}\mathit{n}\left(\mathit{x}\right)+{\mathit{t}\mathit{a}\mathit{n}}^2\left(\mathit{x}\right)}}{\sqrt{\mathit{t}\mathit{a}\mathit{n}\left(\mathit{x}\right)-{\mathit{t}\mathit{a}\mathit{n}}^2\left(\mathit{x}\right)}}\mathit{s}\mathit{i}\mathit{n}\left(\mathit{x}\right)\right)\mathit{d}\mathit{x}$$$$=\frac{1}{2}+\frac{\sqrt{\mathit{\pi }}}{8}(\frac{\mathbf{\Gamma }\left(\frac{1}{4}\right)}{\mathbf{\Gamma }\left(\frac{3}{4}\right)}-\frac{\mathbf{\Gamma }\left(\frac{3}{4}\right)}{\mathbf{\Gamma }\left(\frac{5}{4}\right)})$$ Answered by Ar…

Question Number 133 by sagarwal last updated on 25/Jan/15 $$\mathrm{Evaluate}\int \sqrt{\sin x}dx$$ Answered by gkfichadia last updated on 10/Dec/14 $$$$$$$$$$ \…

Question Number 131189 by Raxreedoroid last updated on 02/Feb/21 $$\int \frac{-sin\left(ln\left(k^x\right)\right)}{\sqrt{k}}dx=??$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 131183 by john_santu last updated on 02/Feb/21 Answered by liberty last updated on 02/Feb/21 $$\frac{\mathrm{dP}}{(32-\mathrm{P})\mathrm{P}}=0.0015\mathrm{dt}$$$$\frac{1}{32}\int [\frac{1}{32-\mathrm{P}}+\frac{1}{\mathrm{P}}]\mathrm{dP}=\int 0.0015\mathrm{dt}$$$$\frac{1}{32}\ln \mid \frac{\mathrm{P}}{32-\mathrm{P}}\mid =0.0015\mathrm{t}+\mathrm{c}$$$$\ln \mid \frac{\mathrm{P}}{32-\mathrm{P}}\mid =0.48\mathrm{t}+\mathrm{C};\frac{\mathrm{P}\left(\mathrm{t}\right)}{32-\mathrm{P}\left(\mathrm{t}\right)}=\lambda {\mathrm{e}}^{0.048\mathrm{t}}$$$$\Leftrightarrow\:\frac{\mathrm{32}−\mathrm{P}\left(\mathrm{t}\right)}{\mathrm{P}\left(\mathrm{t}\right)}\:=\:\frac{\mathrm{1}}{\lambda}\mathrm{e}^{−\mathrm{0}.\mathrm{048t}}…