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Category: Integration

Question-91714

Question Number 91714 by jagoll last updated on 02/May/20 Commented by Tony Lin last updated on 02/May/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \right){e}^{{x}^{\mathrm{2}} } {dx} \\ $$$$=\left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}}…

Show-that-0-1-1-x-1-x-2-dx-ln-4-3-

Question Number 157254 by physicstutes last updated on 21/Oct/21 $$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx}\:=\:\mathrm{ln}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$ Answered by puissant last updated on 21/Oct/21 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Nice-Mathematics-calculation-0-1-tanh-1-x-x-dx-pi-2-4-x-t-2-0-1-tanh-1-t-t-

Question Number 157251 by mnjuly1970 last updated on 21/Oct/21 $$ \\ $$$$\:\:\:\:\:#\:\mathrm{Nice}\:\mathrm{Mathematics}\:# \\ $$$$\:\:\:\:\:\:\:…{calculation}\:… \\ $$$$\:\:\:\:\:\:\:\:\Omega\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \:\left(\sqrt{\:{x}}\:\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\:\pi^{\:\mathrm{2}} }{\mathrm{4}} \\ $$$$\:\:\:−−−−−−−−−−−−− \\ $$$$\:\:\:\:\Omega\::\overset{\sqrt{{x}}\:=\:{t}}…

Prove-that-If-f-x-is-Riemann-integrable-on-a-b-and-M-gt-0-s-t-x-a-b-f-x-0-and-f-x-lt-M-and-1-f-x-lt-M-then-1-f-x-is-Riemann-integrable-on-a-b-

Question Number 26142 by moxhix last updated on 21/Dec/17 $$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{Riemann}\:\mathrm{integrable}\:\mathrm{on}\:\left[{a},{b}\right]\:\mathrm{and} \\ $$$$\:\:\:\:\:\exists{M}>\mathrm{0}\:{s}.{t}.\:\forall{x}\in\left[{a},{b}\right]\:\left({f}\left({x}\right)\neq\mathrm{0}\:{and}\:\mid{f}\left({x}\right)\mid<{M}\:{and}\:\mid\frac{\mathrm{1}}{{f}\left({x}\right)}\mid<{M}\right), \\ $$$$\mathrm{then}\:\frac{\mathrm{1}}{{f}\left({x}\right)}\:\mathrm{is}\:\mathrm{Riemann}\:\mathrm{integrable}\:\mathrm{on}\:\left[{a},{b}\right]. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-26125

Question Number 26125 by offrinshingal last updated on 20/Dec/17 Commented by abdo imad last updated on 21/Dec/17 $$\int_{{R}} \frac{{x}\:{e}^{{irx}} }{\left({x}^{\mathrm{2}} −{k}^{\mathrm{2}} \right)}{dx}\:−\:\int_{{R}} \:\frac{{x}\:{e}^{−{irx}} }{\left({x}^{\mathrm{2}} −\:{k}^{\mathrm{2}}…