Category: Integration

Question Number 64970 by mathmax by abdo last updated on 23/Jul/19 $${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)\:+{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx}\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}}…

Question Number 130485 by benjo_mathlover last updated on 26/Jan/21 $$\:\digamma\:=\:\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{5}\:} \mathrm{ln}\:\left({x}\right)\mathrm{cos}\:\left({x}\right){e}^{−{x}} \:{dx}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $${I}\left({a}\right)=\int_{\mathrm{0}}…

Question Number 130474 by EDWIN88 last updated on 26/Jan/21 $$\mathcal{E}\:=\:\int_{\:\mathrm{0}} ^{\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}} \:\frac{\mathrm{dy}}{\left(\mathrm{1}−\mathrm{y}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} }\: \\ $$ Answered by liberty last updated on 26/Jan/21 Terms of…

Question Number 130448 by physicstutes last updated on 25/Jan/21 $$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:{f}\left(\pi−{x}\right),\:\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\pi} {xf}\left({x}\right){dx}\:=\:\frac{\pi}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi} {f}\left({x}\right){dx}. \\ $$$$\mathrm{please}\:\mathrm{what}\:\mathrm{are}\:\mathrm{different}\:\mathrm{methods}\:\mathrm{to}\:\mathrm{approach}\:\mathrm{this}\:\mathrm{question}? \\ $$ Answered by TheSupreme last updated on 25/Jan/21…

Question Number 64904 by mathmax by abdo last updated on 23/Jul/19 $${calculate}\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\int_{\mathrm{0}} ^{{x}} \:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dydx}\: \\ $$ Commented by ~ À…