Category: Integration

Question Number 144245 by ArielVyny last updated on 23/Jun/21 $${\int }_0^1\frac{x^{2n}}{{(x-1)}^n}dx$$ Answered by mathmax by abdo last updated on 23/Jun/21…

Question Number 78706 by abdomathmax last updated on 20/Jan/20 $$calculate\int {\int }_{{[0,1]}^2}\frac{dxdy}{{(x+y+1)}^2}$$ Answered by mind is power last updated on 20/Jan/20 $$=\int_{\mathrm{0}}…

Question Number 78707 by abdomathmax last updated on 20/Jan/20 $$letI={\int }_0^1\frac{ln(1+x)}{1+x^2}dxand$$$$J=\int {\int }_{{[0,1]}^2}\frac{x}{(1+x^2)(1+xy)}dxdy$$$$findJbytwomethodanddeducethevalueofI$$ Answered by mind…

Question Number 78700 by abdomathmax last updated on 20/Jan/20 $$calculate\int {\int }_D\frac{\mid x-2\mid }{y}dxdywith$$$$D=\{(x,y)\in R^2/0⩽x⩽3and1⩽y⩽e\}$$ Commented by john santu last updated on 20/Jan/20 $$=\:\int_{\mathrm{1}}…

Question Number 144231 by mnjuly1970 last updated on 23/Jun/21 $$\dots ..Nice\dots Calculus$$$$if::$$$$\phi \left(n\right):={\int }_0^1\frac{x^n}{1+x}dx$$$$then::\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{n-1}\phi \left(n\right)}{n}=?$$$$\:\:\:\:\:\:\:…….. \…