Question Number 134811 by bramlexs22 last updated on 07/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)}{\mathrm{tan}\:\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$ Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{set}\:\frac{\mathrm{3x}}{\mathrm{2}}\:=\:\mathrm{t}\:\Rightarrow\:\mathrm{3x}\:=\:\mathrm{2t}\:,\:\begin{array}{|c|c|}{\mathrm{x}=\frac{\pi}{\mathrm{2}}\rightarrow\mathrm{t}=\frac{\mathrm{3}\pi}{\mathrm{4}}}\\{\mathrm{x}=\mathrm{0}\:\rightarrow\mathrm{t}=\mathrm{0}}\\\hline\end{array} \\ $$$$\mathbb{L}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{3}\pi/\mathrm{4}}…
Question Number 69272 by TawaTawa last updated on 22/Sep/19 Answered by $@ty@m123 last updated on 22/Sep/19 $${Let}\:\angle{DPC}=\theta \\ $$$$\Rightarrow\angle{Q}=\theta−\mathrm{30} \\ $$$${Let}\:{CP}={x} \\ $$$${In}\:\bigtriangleup{DCP}, \\ $$$$\mathrm{tan}\:\theta=\frac{\sqrt{\mathrm{3}}}{{x}}\:…\left(\mathrm{1}\right)…
Question Number 3735 by prakash jain last updated on 19/Dec/15 $$\mathrm{Prove} \\ $$$$\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{mn}}{\mathrm{2}^{{m}+{n}} }=\mathrm{4} \\ $$ Commented by prakash jain last…
Question Number 3734 by prakash jain last updated on 19/Dec/15 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{n}}{\mathrm{2}^{{n}} }=? \\ $$ Answered by prakash jain last updated on 19/Dec/15 $${a}_{{n}}…
Question Number 69268 by A8;15: last updated on 22/Sep/19 Answered by mr W last updated on 22/Sep/19 $${x}^{{x}^{\mathrm{20}} } =\mathrm{2}^{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} \\ $$$${x}^{{x}} =\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{20}\sqrt{\mathrm{2}}}} ={a} \\…
Question Number 134801 by faysal last updated on 07/Mar/21 Answered by EDWIN88 last updated on 07/Mar/21 $$\mathrm{13}\theta\:=\:\pi\:\Rightarrow\mathrm{cos}\:\mathrm{13}\theta\:=\:−\mathrm{1} \\ $$$$\mathrm{let}\::\:\mathrm{z}\:=\:\mathrm{cos}\:\theta\:\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta \\ $$$$\mathrm{2z}\:\mathrm{sin}\:\theta\:=\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{cos}\:\mathrm{2}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta \\ $$$$\mathrm{4z}\:\mathrm{sin}\:\theta\:=\:\mathrm{sin}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{4}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta \\ $$$$\mathrm{8z}\:\mathrm{sin}\:\theta\:=\:\mathrm{sin}\:\mathrm{8}\theta\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:\mathrm{5}\theta\:\mathrm{cos}\:\mathrm{6}\theta…
Question Number 134798 by bramlexs22 last updated on 07/Mar/21 $$\mathrm{Binomial}\:\mathrm{theorem} \\ $$Given that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5…
Question Number 69261 by mathmax by abdo last updated on 22/Sep/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{xtanx}\:{dx} \\ $$ Answered by mind is power last updated on 23/Sep/19…
Question Number 134795 by 0731619177 last updated on 07/Mar/21 Answered by EDWIN88 last updated on 07/Mar/21 $$\:\mathrm{noting}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integrand}\:\mathrm{is}\:\mathrm{even}\:\mathrm{function} \\ $$$$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{\infty} \frac{\mathrm{sin}\:\left(\pi\mathrm{x}\right)}{\mathrm{x}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}…
Question Number 69257 by Henri Boucatchou last updated on 21/Sep/19 $$\int_{−\mathrm{2}} ^{\:\:\mathrm{4}} \mid\boldsymbol{{x}}\mid^{\mathrm{2}\boldsymbol{{x}}^{\mathrm{3}} } \boldsymbol{{dx}}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com