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Category: Integration

Question-122469

Question Number 122469 by benjo_mathlover last updated on 17/Nov/20 Commented by benjo_mathlover last updated on 17/Nov/20 $${i}'{m}\:{forgot}\:{the}\:{formula}\:{the}\:\:{average}\:{rate}\:{of} \\ $$$${change}\:{of}\:{the}\:{function}.\:{is}\:{it}\: \\ $$$${A}\left({x}\right)\:=\:\frac{\mathrm{1}}{{b}−{a}}\:\underset{{a}} {\overset{{b}} {\int}}\:{f}\left({x}\right)\:{dx}\:? \\ $$…

x-3-4-x-2-x-2-4-dx-

Question Number 122430 by benjo_mathlover last updated on 17/Nov/20 $$\:\int\:\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }+{x}^{\mathrm{2}} −\mathrm{4}}\:{dx}\: \\ $$ Answered by liberty last updated on 17/Nov/20 $$\:\mathrm{let}\:\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:=\:\omega\:\wedge\:\mathrm{x}^{\mathrm{2}} −\mathrm{4}\:=−\omega^{\mathrm{2}}…

a-2x-1-1-x-1-x-1-x-dx-c-dx-x-x-1-3-b-dx-x-x-1-d-dx-1-x-1-x-x-2-

Question Number 122397 by Ar Brandon last updated on 16/Nov/20 $$\mathrm{a}\backslash\int\frac{\mathrm{2x}+\mathrm{1}}{\mathrm{1}+\mathrm{x}}\sqrt{\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}}\mathrm{dx}\:\:\:\:\:\:\:\:\mathrm{c}\backslash\int\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}}+\sqrt[{\mathrm{3}}]{\mathrm{x}}} \\ $$$$\mathrm{b}\backslash\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}−\mathrm{1}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}\backslash\int\frac{\mathrm{dx}}{\:\left(\mathrm{1}+\mathrm{x}\right)\sqrt{\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} }} \\ $$ Answered by Dwaipayan Shikari last updated on 16/Nov/20 $$\int\frac{{dx}}{{x}+\sqrt{{x}−\mathrm{1}}}…

Question-122366

Question Number 122366 by rs4089 last updated on 16/Nov/20 Answered by mathmax by abdo last updated on 16/Nov/20 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{sin}\left(\mathrm{sinx}\right)}{\mathrm{x}}\mathrm{e}^{\mathrm{cosx}} \mathrm{dx}\:\:\mathrm{the}\:\mathrm{function}\:\mathrm{under}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{even}\:\Rightarrow \\ $$$$\mathrm{2I}=\int_{−\infty} ^{+\infty}…

let-f-t-0-cos-t-1-x-2-1-x-2-dx-with-t-0-find-a-explicit-form-of-f-t-

Question Number 56829 by maxmathsup by imad last updated on 24/Mar/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({t}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right)\: \\ $$ Answered by Smail last updated…