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Category: Integration

Evaluate-5-5-25-x-2-dx-using-an-algebraic-method-Geometrical-mehod-thanks-in-advanced-great-mathematicians-

Question Number 72337 by Rio Michael last updated on 27/Oct/19 $${Evaluate}\:\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\:\right)\:{dx}\:{using} \\ $$$$\Rightarrow\:{an}\:{algebraic}\:{method} \\ $$$$\Rightarrow\:{Geometrical}\:{mehod}\: \\ $$$${thanks}\:{in}\:{advanced}\:{great}\:{mathematicians} \\ $$ Commented by mathmax…

nice-calculus-prove-that-0-1-log-1-x-x-2-dx-2-2-

Question Number 137829 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:…….{nice}\:\:…\:…\:….\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}\::::: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{log}\left(\mathrm{1}−{x}\right)}{{x}}\right)^{\mathrm{2}} {dx}=\mathrm{2}\zeta\left(\mathrm{2}\right)…. \\ $$$$ \\ $$ Answered by EnterUsername last…

If-z-x-is-a-complex-function-is-the-following-true-zdx-z-dx-i-z-dx-

Question Number 6737 by FilupSmith last updated on 19/Jul/16 $$\mathrm{If}\:{z}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{function}, \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{true}: \\ $$$$\int{zdx}=\int\Re\left({z}\right){dx}+{i}\int\Im\left({z}\right){dx} \\ $$ Commented by prakash jain last updated on 19/Jul/16 $$\mathrm{Yes}.\:\mathrm{Since}\:{i}\:\mathrm{is}\:\mathrm{simply}\:\mathrm{a}\:\mathrm{constant}.…

mathematical-analysis-evaluate-0-1-ln-2-1-x-2-x-

Question Number 137799 by mnjuly1970 last updated on 06/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…..\:{mathematical}\:..\:…\:…\:{analysis}…. \\ $$$$\:\:\:\:\:\:\:{evaluate}\:::\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}}\right)=? \\ $$$$ \\ $$ Answered…