Category: Integration

Question Number 43937 by abdo.msup.com last updated on 18/Sep/18 $$calculate{\int }_0^1\frac{2x+1}{\sqrt{x^2-2x+5}}dx$$ Commented by maxmathsup by imad last updated on 19/Sep/18 $${let}\:{A}\:=\:\int_{\mathrm{0}}…

Question Number 43935 by abdo.msup.com last updated on 18/Sep/18 $$findf\left(a\right)={\int }_0^{\mathrm{\infty }}\frac{1-{cos}^2\left(ax\right)}{x^2}dx$$$$2)calculate{f}^{{}^{\prime }}\left(a\right).$$ Commented by maxmathsup by imad last…

Question Number 43923 by pieroo last updated on 17/Sep/18 $$\mathrm{A}\mathrm{curve}\mathrm{passes}\mathrm{through}\mathrm{the}\mathrm{point}(1,-11)\mathrm{and}\mathrm{its}$$$$\mathrm{gradient}\mathrm{at}\mathrm{any}\mathrm{point}\mathrm{is}\mathbf{a}{\mathrm{x}}^2+\mathbf{b},\mathrm{where}\mathbf{a}\mathrm{and}\mathbf{b}\mathrm{are}$$$$\mathrm{constants}.\mathrm{The}\mathrm{tangent}\mathrm{to}\mathrm{the}\mathrm{curve}\mathrm{at}\mathrm{the}\mathrm{point}$$$$(2,-16)\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{the}\mathbf{x}-\mathrm{axis}.\mathrm{Find}$$$$\mathrm{i}.\mathrm{the}\mathrm{values}\mathrm{of}\mathbf{a}\mathrm{and}\mathbf{b}$$$$\mathrm{ii}.\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{curve}$$ Answered by…

Question Number 109457 by shahria14 last updated on 23/Aug/20 Answered by Dwaipayan Shikari last updated on 23/Aug/20 $$\int {sin}^{3}x(1-{cos}^{2}x)dx$$$$\int{sin}^{\mathrm{3}} {x}−\int{sin}^{\mathrm{3}} {xcos}^{\mathrm{2}} {x}…

Question Number 43914 by maxmathsup by imad last updated on 17/Sep/18 $$find\int \frac{x}{\sqrt{1+cosx}}dx.$$ Commented by maxmathsup by imad last updated on 19/Sep/18 $${let}\:{A}\:=\:\int\:\:\:\:\:\frac{{x}}{\:\sqrt{\mathrm{1}+{cosx}}}{dx}\:{we}\:{have}\:{A}\:=\:\int\:\:\:\frac{{x}}{\:\sqrt{\mathrm{2}{cos}^{\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)}}{dx}…