Category: Integration

Question Number 134672 by mnjuly1970 last updated on 06/Mar/21 $$\dots .nicecalculus\dots$$$$provethat:$$$$\sqrt{5\pi }⩽{\int }_0^{\frac{\pi }{3}}\frac{9\sqrt{3}}{2\pi }\sqrt{8sin\left(x\right)-sin\left(2x\right)}dx⩽\sqrt{6\pi }$$$$\dots m.n\dots .$$ Terms of Service Privacy Policy…

Question Number 134660 by benjo_mathlover last updated on 06/Mar/21 $$\mathcal{M}=\int \frac{dx}{2\cos x+3\sin x}$$ Answered by EDWIN88 last updated on 06/Mar/21 $$\mathrm{Let}\{\begin{array}{l}2=\mathrm{r}\sin \alpha \\ 3=\mathrm{r}\cos \alpha \end{array}\Rightarrow {\mathrm{r}}^2=13;\mathrm{r}=\sqrt{13}$$$$\:\mathrm{and}\:\mathrm{tan}\:\alpha\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:,\therefore\:\alpha\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right) \…

Question Number 69110 by Fawole last updated on 20/Sep/19 $$Evaluate{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{cos\left(x\right)}{x^2+1}dx$$ Commented by mathmax by abdo last updated on 20/Sep/19 $$\:\:{let}\:{I}\:=\int_{−\infty}…

Question Number 134636 by bobhans last updated on 06/Mar/21 $$\mathcal{INTEGRAL}$$$$\left(1\right){\int }_0^{\ln 2}{x}^{-2}.e^{-\frac{1}{x}}dx=?$$$$\left(2\right)\int \frac{\sin \mathrm{x}+\cos \mathrm{x}}{\sin {}^4\mathrm{x}+\cos {}^4\mathrm{x}}\mathrm{dx}=?$$ Answered by benjo_mathlover…

Question Number 134601 by abdullahquwatan last updated on 05/Mar/21 $$\int 3\left(\sqrt{\mathrm{x}+\frac{4}{\sqrt{\mathrm{x}}}}\right)\mathrm{dx}$$ Answered by bobhans last updated on 06/Mar/21 $$\sqrt{\frac{\mathrm{x}\sqrt{\mathrm{x}}+4}{\sqrt{\mathrm{x}}}}=\frac{\sqrt{\mathrm{x}\sqrt{\mathrm{x}}+4}}{\sqrt[4]{\mathrm{x}}}$$$$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{t}^{\mathrm{4}} \:\Rightarrow\mathrm{dx}\:=\:\mathrm{4t}^{\mathrm{3}} \:\mathrm{dt} \…