Category: Integration

Question Number 48494 by maxmathsup by imad last updated on 24/Nov/18 $$find{A}_n={\int }_0^{\frac{\pi }{2}}\frac{1-cos(n+1)x}{2sin\left(\frac{x}{2}\right)}dx.$$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/Nov/18 $${A}_{{n}}…

Question Number 48484 by Meritguide1234 last updated on 24/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 24/Nov/18 $$tryingtosolve$$$$letinplaceof\sqrt{3}puttingaa=\sqrt{3}$$$$findingthevaluesofxsothat$$$$sinax=sinx$$$${ax}={k}\pi+\left(−\mathrm{1}\right)^{{k}}…

Question Number 179510 by Acem last updated on 30/Oct/22 $$Evaluate\int e^{4x}\sqrt{\frac{1}{e^{-2x}}+1}dx$$ Commented by cortano1 last updated on 30/Oct/22 $$\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}\:=\:\lambda\:\Rightarrow\mathrm{e}^{\mathrm{2x}} =\lambda^{\mathrm{2}} −\mathrm{1}…

Question Number 179478 by Acem last updated on 29/Oct/22 $$Find{\int }_0^{\frac{1}{6}}\frac{1}{x^{-5}{(36x^2+1)}^{\frac{3}{2}}}dx$$ Answered by MJS_new last updated on 29/Oct/22 $$\int\frac{{dx}}{{x}^{−\mathrm{5}}…

Question Number 113910 by bobhans last updated on 16/Sep/20 $$\left(1\right)\underset{0}{\stackrel{\pi }{\int }}\frac{\sin {}^{4}x}{{(1+\cos x)}^2}dx?$$$$\left(2\right)\underset{x\to \mathrm{\infty }}{\lim }\frac{\sqrt{1-\cos \left(\frac{2\pi }{x}\right)}}{\frac{1}{x}}?$$ Answered by bemath last updated on…