Category: Integration

Question Number 174628 by cortano1 last updated on 06/Aug/22 $$\mathrm{\Omega }=\int \frac{x}{1+\csc x}dx=?$$ Commented by infinityaction last updated on 06/Aug/22 $$\int \frac{x}{1+\csc x}dx=\int \frac{xs\mathrm{in}x}{1+\sin x}dx$$$$=\int x\frac{1+\sin x-1}{1+\sin x}dx=\int (x-\frac{x}{1+\sin x})dx$$$$\Omega\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−\int\frac{{x}}{\underset{{I}}…

Question Number 109086 by bobhans last updated on 21/Aug/20 $$\underrightarrow{\mathrm{♭}}\underrightarrow{o}\mathrm{♭}\underset{⊸}{han}\underset{⊸}{s}$$$$\left(1\right)(x^2{e}^{-\frac{y}{x}}+y^2)dx=xydy$$$$\left(\mathrm{2}\right)\left(\frac{{f}\left({x}\right)}{{x}}\right)'\:=\:{x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } \:;\:{f}\left(\mathrm{1}\right)\:=\:\frac{\mathrm{1}}{{e}}\: \…

Question Number 43551 by peter frank last updated on 11/Sep/18 $$evaluate\int \frac{1}{\cos (x-a)\cos (x-b)}dx$$ Answered by MJS last updated on 12/Sep/18 $$\int \frac{dx}{\cos (x-a)\cos (x-b)}=$$$$[t=x-a\to dx=dt]$$$$=\int\frac{{dt}}{\mathrm{cos}\:{t}\:\mathrm{cos}\left({t}+{a}−{b}\right)}=…

Question Number 43538 by abdo.msup.com last updated on 11/Sep/18 $$calculate\int {\int }_{\frac{x^2}{a^2}+\frac{y^2}{b^2}⩽1}(x^2-y^2)dxdywhit$$$$a>0andb>0.$$ Commented by maxmathsup by…

Question Number 43535 by maxmathsup by imad last updated on 11/Sep/18 $$1)findthevalueof{\int }_{\frac{\pi }{4}}^{\frac{\pi }{3}}\sqrt{1+tan\theta }d\theta .$$ Commented by MJS last updated on 12/Sep/18 $$\mathrm{it}'\mathrm{s}\:\mathrm{possible}\:\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{a}\:\mathrm{long}\:\mathrm{way} \…