Question Number 70369 by ahmadshahhimat775@gmail.com last updated on 03/Oct/19 Commented by MJS last updated on 03/Oct/19 $$\mathrm{see}\:\mathrm{question}\:\mathrm{69588} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 70361 by mind is power last updated on 03/Oct/19 $${Hello}\: \\ $$$${si}\left({x}\right)=−\int_{{x}} ^{\infty} \frac{{sin}\left({x}\right)}{{x}}{dx} \\ $$$${show}\:\int_{\mathrm{0}} ^{+\infty} {x}^{{a}−\mathrm{1}} {si}\left({x}\right){dx}=−\frac{\Gamma\left({a}\right){sin}\left(\frac{\pi{a}}{\mathrm{2}}\right)}{{a}} \\ $$$${hint}\:{ipp}\:+{complex}\:{Analysis} \\ $$…
Question Number 135888 by mnjuly1970 last updated on 16/Mar/21 Answered by mindispower last updated on 19/Mar/21 $${recal}\:\chi_{\mathrm{2}} \left({x}\right)=\frac{{li}_{\mathrm{2}} \left({x}\right)−{li}_{\mathrm{2}} \left(−{x}\right)}{\mathrm{2}},{chi}\:{function} \\ $$$${we}\:{have}\:\chi_{\mathrm{2}} \left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)+\chi_{\mathrm{2}} \left({x}\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{8}}+\frac{{ln}\left({x}\right){ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)}{\mathrm{2}}…
Question Number 135872 by Engr_Jidda last updated on 16/Mar/21 $${Evaluate}\:\oint_{{c}} {ydy}\:{where}\:\:{c}\:{is}\:{a}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4} \\ $$ Answered by mathmax by abdo last updated on 16/Mar/21 $$\mathrm{y}\:=\xi\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}}…
Question Number 135867 by liberty last updated on 16/Mar/21 $$\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{4}{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \left({x}\right)=\mathrm{2sin}\:\left(\mathrm{4}{x}\right)\mathrm{cos}\:^{\mathrm{2}} \left({x}\right) \\ $$$$ \\ $$ Answered by EDWIN88 last updated on 16/Mar/21 $$\mathrm{recall}\:\mathrm{cos}\:^{\mathrm{2}}…
Question Number 135820 by Ar Brandon last updated on 16/Mar/21 $$\mathrm{Let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {e}^{−{t}^{\mathrm{2}} } {dt}\:, \\ $$$$\mathrm{Prove}\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}^{\mathrm{2}} +{f}\left({x}\right)} {dx}={e}^{\frac{\sqrt{\pi}}{\mathrm{2}}} −\mathrm{1}. \\ $$ Answered…
Question Number 70262 by mathmax by abdo last updated on 02/Oct/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cosx}\right){dx}\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({sinx}\right){dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 135784 by benjo_mathlover last updated on 16/Mar/21 $${Given}\:\begin{cases}{{f}\left(\mathrm{3}\right)=\mathrm{4}\:,\:{f}\:'\left(\mathrm{3}\right)=−\mathrm{2}}\\{{f}\left(\mathrm{8}\right)=\mathrm{5}\:,\:{f}\:'\left(\mathrm{8}\right)=\mathrm{3}}\end{cases} \\ $$$${find}\:\int_{\mathrm{3}} ^{\:\mathrm{8}} \:{x}\:{f}\:''\left({x}\right)\:{dx}\:. \\ $$ Answered by Ar Brandon last updated on 16/Mar/21 $$\int_{\mathrm{3}}…
Question Number 135777 by mathmax by abdo last updated on 15/Mar/21 $$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{calculate}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{e}^{\mathrm{n}^{\mathrm{2}} } \mathrm{U}_{\mathrm{n}} \\ $$ Answered by mathmax…
Question Number 70237 by mathmax by abdo last updated on 02/Oct/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:{with}\:\alpha\:{real} \\ $$ Commented by mind is power last updated on…