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Category: Differentiation

Question-155203

Question Number 155203 by nadovic last updated on 26/Sep/21 Answered by TheHoneyCat last updated on 29/Sep/21 $$\mathrm{let}\:\mathrm{O}\:\mathrm{be}\:\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{let}\:\mathrm{A}\:\mathrm{be}\:\mathrm{a}\:\mathrm{vertice}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle} \\ $$$$\mathrm{let}\:\theta\:\mathrm{be}\:\mathrm{an}\:\mathrm{angle}\:\left(\mathrm{in}\:\mathrm{radian}\right)\:\mathrm{between}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{axis}\:\left(\mathrm{O}{z}\:\mathrm{or}\:\mathrm{O}{y}\right)\:\mathrm{and}\:\mathrm{the}\:\left(\mathrm{OA}\right)\:\mathrm{line} \\ $$$$…

the-particular-integral-of-the-differential-equation-f-D-y-e-ax-where-f-D-D-a-g-D-g-a-0-is-

Question Number 23522 by gopikrishnan005@gmail.com last updated on 01/Nov/17 $${the}\:{particular}\:{integral}\:{of}\:{the}\:{differential}\:{equation}\:{f}\left({D}\right){y}={e}^{{ax}} {where}\:{f}\left({D}\right)=\left({D}−{a}\right){g}\left({D}\right),{g}\left({a}\right)\neq\mathrm{0}\:{is} \\ $$ Commented by 1kanika# last updated on 26/Nov/17 $$\mathrm{xe}\Lambda\mathrm{ax}/\mathrm{g}\left(\mathrm{a}\right) \\ $$ Terms of…

prove-that-0-sin-3-x-ln-x-x-dx-pi-8-2-ln-3-m-n-

Question Number 154478 by mnjuly1970 last updated on 18/Sep/21 $$ \\ $$$$ \\ $$$$\:\:{prove}\:{that}\:# \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}^{\:\mathrm{3}} \left(\:{x}\:\right).{ln}\left(\:{x}\:\right)}{{x}}\:{dx}\:\overset{?} {=}\:\frac{\pi}{\mathrm{8}}\:\left(−\mathrm{2}\gamma\:+{ln}\left(\mathrm{3}\right)\right)\:…..\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\: \\ $$$$ \\…