Category: Integration

Question Number 55274 by maxmathsup by imad last updated on 20/Feb/19 $$let\phi \left(a\right)={\int }_1^{\sqrt{3}}arctan\left(\frac{a}{x}\right)dx$$$$1)calculate\phi \left(a\right)intermsofa$$$$2)calculate{\phi }^{{}^{\prime }}\left(a\right)atformofintegral.$$$$3)determine{\phi }^{\left(n\right)}\left(a\right)atformofintegral.$$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{3}}}…

Question Number 186347 by normans last updated on 03/Feb/23 $$$$$$\underset{-2}{\stackrel{2}{\int }}\frac{{\mathit{x}}^5-1+2}{{\mathit{x}}^4+\mathit{x}-2}\mathit{d}\mathit{x}$$$$$$ Commented by Frix last updated…

Question Number 55271 by maxmathsup by imad last updated on 20/Feb/19 $$1)letf\left(x\right)={\int }_0^{2\pi }\frac{cost}{3+sin\left(xt\right)}dt$$$$findaexplicitformoff\left(x\right)$$$$2)calculateg\left(x\right)={\int }_0^{2\pi }\frac{tcos\left(xt\right)cost}{{(3+sin\left(xt\right))}^2}dt$$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cost}}{\mathrm{3}+{sint}}\:\:{and}\:\:\:\int_{\mathrm{0}}…

Question Number 186321 by Mingma last updated on 03/Feb/23 Answered by normans last updated on 03/Feb/23 $${\int }_1^{e^{(\mathit{n}+1)}}\mathit{l}\mathit{o}\mathit{g}\left(\mathit{x}\right)={\mathit{e}}^{\mathit{n}+1}(\mathit{l}\mathit{o}\mathit{g}\left({\mathit{e}}^{\mathit{n}+1}\right)-1+1$$$$\boldsymbol{{for}}\:\boldsymbol{{e}}^{\boldsymbol{{n}}} \geqslant\mathrm{0}\wedge\left(\boldsymbol{{e}}^{\boldsymbol{{n}}+\mathrm{1}}…

Question Number 55237 by peter frank last updated on 19/Feb/19 $${\int }_0^3{\int }_1^2({\mathrm{x}}^3+{\mathrm{y}}^2)\mathrm{dxdy}$$ Commented by Abdo msup. last updated…