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Category: Integration

Number-of-straight-lines-which-satisfy-the-differential-equation-dy-dx-x-dy-dx-2-y-0-is-

Question Number 42215 by rahul 19 last updated on 20/Aug/18 $$\mathrm{Number}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{{dx}}\:+\:{x}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −\:{y}\:=\mathrm{0}\:{is}\:? \\ $$ Commented by rahul 19 last updated on…

let-A-p-0-sin-px-e-x-1-dx-with-p-gt-0-1-give-A-p-at-form-of-serie-2-give-A-1-at-form-of-serie-

Question Number 42191 by maxmathsup by imad last updated on 19/Aug/18 $${let}\:{A}_{{p}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({px}\right)}{{e}^{{x}} −\mathrm{1}}\:{dx}\:\:{with}\:{p}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){give}\:{A}_{{p}} \:\:{at}\:{form}\:{of}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{give}\:{A}_{\mathrm{1}} \:{at}\:{form}\:{of}\:{serie}\:. \\ $$ Commented…

BeMath-1-0-x-1-x-3-dx-2-lim-x-0-sin-pi-cos-2-x-x-2-3-If-g-x-1-x-and-g-f-x-3-2-x-x-find-f-x-

Question Number 107706 by bemath last updated on 12/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\sqrt{{x}}}{\mathrm{1}+{x}^{\mathrm{3}} }\:{dx}\:? \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{{x}^{\mathrm{2}} }\: \\ $$$$\left(\mathrm{3}\right)\:{If}\:{g}\left({x}\right)=\:\mathrm{1}+\sqrt{{x}}\:{and}\:\left({g}\circ{f}\right)\left({x}\right)=\mathrm{3}+\mathrm{2}\sqrt{{x}}\:+{x} \\ $$$$\:\:\:{find}\:{f}\left({x}\right) \\…

BeMath-0-1-x-1-x-1-ln-x-dx-

Question Number 107695 by bemath last updated on 12/Aug/20 $$\:\:\:\spadesuit\mathcal{B}{e}\mathcal{M}{ath}\spadesuit \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\mathrm{ln}\:{x}}\:{dx}\:?\: \\ $$ Answered by mnjuly1970 last updated on 12/Aug/20 $${ans}:={ln}\left(\frac{\mathrm{2}}{\pi}\right)\: \\…

Question-107656

Question Number 107656 by bemath last updated on 12/Aug/20 Answered by john santu last updated on 12/Aug/20 $$\:\:\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$$\:\begin{cases}{\lambda=\mathrm{1}+{x}\sqrt{{x}}}\\{{dx}=\frac{\mathrm{2}{d}\lambda}{\mathrm{3}\sqrt{{x}}}}\end{cases} \\ $$$${I}=\int\:\sqrt{{x}}\:\sqrt{\mathrm{1}+{x}\sqrt{{x}}\:}\:{dx}\: \\ $$$${I}=\:\int\:\sqrt{{x}}\:\sqrt{\lambda}\:\left(\frac{\mathrm{2}{d}\lambda}{\mathrm{3}\sqrt{{x}}}\right)=\int\frac{\mathrm{2}}{\mathrm{3}}\lambda^{\frac{\mathrm{1}}{\mathrm{2}}} \:{d}\lambda…