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Category: Integration

find-the-common-area-of-x-2-3-y-2-1-x-2-y-2-3-1-

Question Number 57821 by behi83417@gmail.com last updated on 12/Apr/19 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{common}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{of}}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\mathrm{3}}+\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{1}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\frac{\boldsymbol{\mathrm{y}}^{\mathrm{2}} }{\mathrm{3}}=\mathrm{1}}\end{cases} \\ $$ Answered by MJS last updated on 13/Apr/19…

If-y-Arcsin-x-x-1-x-y-p-x-y-q-x-1-find-0-1-p-x-q-x-dx-p-q-are-two-pllynomils-

Question Number 188889 by mnjuly1970 last updated on 08/Mar/23 $$ \\ $$$$\:\:{If},\:{y}=\:\frac{\:{Arcsin}\left(\sqrt{{x}}\:\right)}{\:\sqrt{\:{x}\:\left(\mathrm{1}−{x}\:\right)}}\:\:\Rightarrow \\ $$$$\:\:\:{y}'\:.{p}\left({x}\right)\:+\:{y}\:.{q}\left({x}\right)=\:\mathrm{1} \\ $$$$ \\ $$$$\:\:\:{find}\:,\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {p}\left({x}\right).{q}\left({x}\right){dx}=? \\ $$$$\:\:\:\:{p}\:,\:{q}\:\:{are}\:{two}\:{pllynomils}… \\ $$$$ \\…

a-1-e-x-1-e-x-1-2-dx-b-lnx-1-x-c-e-e-sin-lnx-dx-

Question Number 57819 by behi83417@gmail.com last updated on 12/Apr/19 $$\boldsymbol{\mathrm{a}}.\:\:\int\:\:\:\left[\frac{\mathrm{1}−\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}+\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} }\right]\:^{\frac{\mathrm{1}}{\mathrm{2}}} \:\boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{b}}.\:\:\:\:\:\int\:\:\frac{\boldsymbol{\mathrm{lnx}}}{\:\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}}}=? \\ $$$$\boldsymbol{\mathrm{c}}.\:\:\:\:\:\:\:\underset{\:\sqrt{\boldsymbol{\mathrm{e}}}} {\overset{\:\:\:\:\:\boldsymbol{\mathrm{e}}} {\int}}\:\:\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{lnx}}\right)\boldsymbol{\mathrm{dx}}=? \\ $$ Commented by Abdo msup.…

Question-188861

Question Number 188861 by Shlock last updated on 08/Mar/23 Answered by cortano12 last updated on 08/Mar/23 $$\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\mathrm{x}\:\mathrm{d}\left(\mathrm{f}\:'\left(\mathrm{x}\right)\right)=\:\left[\:\mathrm{x}\:\mathrm{f}\:'\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}\right)\:\right]_{\mathrm{0}} ^{\mathrm{4}} \\ $$$$\:=\:\left[\mathrm{4}\:\mathrm{f}\:'\left(\mathrm{4}\right)−\mathrm{f}\left(\mathrm{4}\right)+\mathrm{f}\left(\mathrm{0}\right)\right] \\ $$$$\:=\:\mathrm{4}.\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}+\mathrm{3}\:=\:\mathrm{3}\: \\…

sinx-x-dx-

Question Number 123331 by 676597498 last updated on 24/Nov/20 $$\int\:\frac{{sinx}}{{x}}\:{dx} \\ $$ Answered by MJS_new last updated on 25/Nov/20 $$\int\frac{\mathrm{sin}\:{x}}{{x}}{dx}=\mathrm{Si}\:\left({x}\right)\:+{C} \\ $$$$\mathrm{Si}\:\left({x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{Integral}\:\mathrm{Sinus}.\:\mathrm{search}\:\mathrm{for}\:\mathrm{it}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{www} \\…