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Category: Integration

Question-47088

Question Number 47088 by Meritguide1234 last updated on 04/Nov/18 Answered by MJS last updated on 04/Nov/18 $${x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0} \\ $$$${x}=−\frac{{a}}{\mathrm{2}}\pm\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}{b}}}{\mathrm{2}}\:\Rightarrow\:\alpha=−\frac{{a}}{\mathrm{2}}−\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}{b}}}{\mathrm{2}};\:\beta=−\frac{{a}}{\mathrm{2}}+\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{4}{b}}}{\mathrm{2}\left(\right.} \\ $$$${bx}^{\mathrm{2}}…

number-theory-Question-If-a-b-c-N-then-prove-a-b-c-a-b-c-m-n-july-970-

Question Number 112613 by mnjuly1970 last updated on 08/Sep/20 $$\:\:\:\:\:….{number}\:{theory}… \\ $$$$\:\:\:\:\:\:\:{Question}\::\:\:\:\:\:\:\mathrm{I}{f}\:\:\:{a}\:,\:{b}\:,\:{c}\:\:\in\:\mathbb{N}\:\:\:;\:{then}\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}!\ast{b}!\ast{c}!\mid\left({a}+{b}+{c}\right)!\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}\:.\:{july}\:\mathrm{970}# \\…

let-v-n-a-1-n-n-1-a-x-2-arctan-1-a-x-dx-with-a-gt-0-1-determine-a-explicit-form-of-v-n-a-2-study-the-convergence-of-n-v-n-a-3-calculate-v-n-1-and-n-v-n-1-

Question Number 47065 by maxmathsup by imad last updated on 04/Nov/18 $${let}\:{v}_{{n}} \left({a}\right)=\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\left(\mathrm{1}−\frac{{a}}{{x}^{\mathrm{2}} }\right){arctan}\left(\mathrm{1}+\frac{{a}}{{x}}\right){dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{v}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\sum_{{n}} \:{v}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{3}\right){calculate}\:{v}_{{n}}…

find-x-1-x-1-dx-

Question Number 47062 by maxmathsup by imad last updated on 04/Nov/18 $${find}\:\int\:\:\:\sqrt{\frac{\sqrt{{x}}−\mathrm{1}}{\:\sqrt{{x}}+\mathrm{1}}}{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 04/Nov/18 $${t}^{\mathrm{2}} ={x}\:\:\:{dx}=\mathrm{2}{tdt} \\ $$$$\int\sqrt{\frac{{t}−\mathrm{1}}{{t}+\mathrm{1}}}\:×\mathrm{2}{tdt}…

let-f-a-1-atan-x-dx-1-find-a-explicit-form-of-f-a-2-calculate-1-2tan-x-dx-

Question Number 47061 by maxmathsup by imad last updated on 04/Nov/18 $${let}\:\:{f}\left({a}\right)\:=\int\:\:\:\sqrt{\mathrm{1}+{atan}\left({x}\right)}{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int\:\:\sqrt{\mathrm{1}+\mathrm{2}{tan}\left({x}\right)}{dx}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

find-dx-1-cos-x-cos-2x-

Question Number 47059 by maxmathsup by imad last updated on 04/Nov/18 $$\:{find}\:\int\:\:\frac{{dx}}{\mathrm{1}+{cos}\:{x}\:+{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by maxmathsup by imad last updated on 06/Nov/18 $${let}\:{A}\:=\int\:\:\:\frac{{dx}}{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)}\:=\:\int\:\:\frac{{dx}}{\mathrm{1}+{cos}\left({x}\right)+\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}}…

let-f-x-0-1-dt-2-ch-xt-1-find-a-explicit-form-of-f-x-2-calculate-g-x-0-1-tsh-xt-2-ch-xt-2-dt-3-find-the-value-of-0-1-dt-2-ch-3t-and-0-1-tsh-3t-

Question Number 47060 by maxmathsup by imad last updated on 04/Nov/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left({xt}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{tsh}\left({xt}\right)}{\left(\mathrm{2}+{ch}\left({xt}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left(\mathrm{3}{t}\right)}\:{and}\:\:\int_{\mathrm{0}}…