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Question-113668

Question Number 113668 by mohammad17 last updated on 14/Sep/20 Answered by john santu last updated on 14/Sep/20 $${If}\:\int_{−\mathrm{2}} ^{\mathrm{6}} \left({f}\left({x}\right)+\mathrm{3}\right){dx}\:=\:\mathrm{32}\:\rightarrow\int_{−\mathrm{2}} ^{\mathrm{6}} {f}\left({x}\right){dx}+\mathrm{3}\left(\mathrm{8}\right)=\mathrm{32} \\ $$$$\:\int_{−\mathrm{2}} ^{\mathrm{6}}…

46-2-60-hi-sir-plx-help-me-

Question Number 48111 by ggny last updated on 19/Nov/18 $$\left(−\mathrm{46}−×\right)/\left(−\mathrm{2}\right)=\mathrm{60}\:\: \\ $$$${hi}\:{sir}\:{plx}\:{help}\:{me} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$\frac{−\mathrm{46}−{x}}{−\mathrm{2}}=\mathrm{60} \\ $$$$−\mathrm{46}−{x}=−\mathrm{120} \\…

Prove-that-there-exists-M-gt-0-such-that-for-any-positive-integers-n-we-have-1-2-n-1-M-

Question Number 113641 by ZiYangLee last updated on 14/Sep/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:{M}>\mathrm{0}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{positive}\:\mathrm{integers}\:{n},\:\mathrm{we}\:\mathrm{have} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{…+\sqrt{{n}+\mathrm{1}}}}}\leqslant{M} \\ $$ Commented by mr W last updated on 14/Sep/20 $${A}_{{n}}…

Question-179137

Question Number 179137 by yaslm last updated on 25/Oct/22 Answered by MJS_new last updated on 26/Oct/22 $$\int\frac{\mathrm{sin}\:\mathrm{3}{x}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\:\rightarrow\:{dx}=\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}\right] \\ $$$$=−\int\frac{{t}\left({t}^{\mathrm{2}} −\mathrm{3}\right)}{\left({t}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} \sqrt{{t}^{\mathrm{2}}…

prove-the-following-integral-0-pi-2-x-2-sinx-dx-2piG-7-2-3-0-1-ln-x-1-x-2-x-1-x-2-2-x-1-x-2-dx-pi-2-2-0-e-x-lnx-1-e-2x-dx-pi-2-ln-3-4-

Question Number 113589 by mathdave last updated on 14/Sep/20 $${prove}\:{the}\:{following}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}} }{\mathrm{sin}{x}}{dx}=\mathrm{2}\pi{G}−\frac{\mathrm{7}}{\mathrm{2}}\zeta\left(\mathrm{3}\right) \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left[\frac{{x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{x}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\right]^{\mathrm{2}} \frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}} }{dx}=\frac{.\pi^{\mathrm{2}} }{\mathrm{2}} \\…