Question Number 13623 by Tinkutara last updated on 21/May/17 $$\mathrm{Evaluate}:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} {e}^{{x}} \:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{4}}\:+\:\frac{{x}}{\mathrm{2}}\right){dx} \\ $$ Answered by ajfour last updated on 21/May/17 $${I}=\int_{\mathrm{0}} ^{\:\:\mathrm{2}\pi} {e}^{{x}}…
Question Number 79128 by ~blr237~ last updated on 22/Jan/20 $${Find}\:{out}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{t}+{t}^{\mathrm{2}} \right){dt} \\ $$$${Then}\:{deduce}\:{the}\:{value}\:{of}\:\:\:{A}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\begin{pmatrix}{\mathrm{2}{n}+\mathrm{1}}\\{{n}}\end{pmatrix}} \\ $$ Commented by mathmax by abdo last…
Question Number 144662 by mnjuly1970 last updated on 27/Jun/21 $$\:\:\:\:\:\:\:………..\:\:\mathrm{Calculus}……….. \\ $$$$\:\mathrm{In}\:\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\:: \\ $$$$\hat {\mathrm{B}}\:=\:\mathrm{2}\:\hat {\mathrm{C}}\:\:\:\:,\:\:{a}\:\:=\:\lambda\:{b}\:\:\:{then}\:{specify} \\ $$$$\:{the}\:\:{limits}\:{of}\:{the}\:{changes}\:\:\:'\:\:\lambda\:\:'\:\:: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$ \\ $$…
Question Number 144636 by liberty last updated on 27/Jun/21 $$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{regions} \\ $$$$\:\:\mathrm{enclosed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{and}\:\mathrm{curves} \\ $$$$\:\:\:\mathrm{x}=\mathrm{y}^{\mathrm{2}} −\mathrm{1}\:\mathrm{and}\:\mathrm{x}=\mid\mathrm{y}\mid\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }\: \\ $$$$ \\ $$ Answered by imjagoll last updated…
Question Number 144638 by liberty last updated on 27/Jun/21 $$\mathrm{Triangle}\:\mathrm{AOC}\:\mathrm{inscribed} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{region}\:\mathrm{cut}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{by}\:\mathrm{the} \\ $$$$\mathrm{line}\:\mathrm{y}=\mathrm{a}^{\mathrm{2}} \:.\mathrm{Find}\:\mathrm{the}\:\mathrm{limit} \\ $$$$\mathrm{of}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{triangle}\:\mathrm{to}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{parabolic}\:\mathrm{region}\:\mathrm{as}\:\mathrm{a}\:\mathrm{approaches} \\…
Question Number 79100 by mathmax by abdo last updated on 22/Jan/20 $${calculate}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo…
Question Number 79096 by mathmax by abdo last updated on 22/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }{dx} \\ $$ Commented by mind is power last updated on…
Question Number 79092 by mathmax by abdo last updated on 22/Jan/20 $${find}\:\int_{−\infty} ^{+\infty} \:\:\frac{{e}^{−{x}^{\mathrm{2}} } {arctan}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$ Terms of Service Privacy Policy…
Question Number 79095 by mathmax by abdo last updated on 22/Jan/20 $${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({x}\right){sin}\left(\mathrm{2}{x}\right)….{sin}\left({nx}\right)}{{x}^{{n}} }{dx}\:\:{with}\:{n}\geqslant\mathrm{2}\:{integr} \\ $$ Commented by mind is power last updated…
Question Number 79094 by mathmax by abdo last updated on 22/Jan/20 $${find}\:{I}_{{a},{b}} \:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({ax}\right){sin}\left({bx}\right)}{{x}^{\mathrm{2}} }{dx}\:\:\:{witha}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$ Answered by mind is power last updated…