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Category: Differentiation

Calculate-If-0-1-tanh-1-x-3-x-dx-2-then-M-N-

Question Number 166690 by mnjuly1970 last updated on 25/Feb/22 $$ \\ $$$$\:\:\:\:\:\:\:\:\:{Calculate}\: \\ $$$$\:\:\:\:\:{If}\:\:,\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \left(\:{x}^{\:\mathrm{3}} \:\right)}{{x}}\:{dx}\:=\:\alpha.\zeta\left(\:\mathrm{2}\right)\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:,\:\:\:\:\:\alpha\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\mathscr{M}.\mathscr{N}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$ \\…

Question-35537

Question Number 35537 by Raj Singh last updated on 20/May/18 Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18 $${f}\left({x}\right)={y}={x}^{\mathrm{2}} \:\: \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1}^{\mathrm{2}} =\mathrm{1}\:\:\:\:{and}\:{f}\left(\mathrm{2}\right)=\mathrm{2}^{\mathrm{2}} =\mathrm{4} \\ $$$${slope}\:{m}=\frac{{f}\left(\mathrm{2}\right)−{f}\left(\mathrm{1}\right)}{\mathrm{2}−\mathrm{1}}=\mathrm{3}…

Question-35461

Question Number 35461 by Raj Singh last updated on 19/May/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/May/18 $${x}.\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{1}+{y}\right)^{−\mathrm{1}/\mathrm{2}} ×\frac{{dy}}{{dx}}+{y}×\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{1}+{x}\right)^{−\mathrm{1}/\mathrm{2}} \\ $$$$ \\ $$ Terms of…