Menu Close

Author: Tinku Tara

I-0-1-sin-1-x-1-x-x-2-dx-pi-4-ln3-

Question Number 136643 by Ñï= last updated on 24/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}^{−\mathrm{1}} \sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}+{x}^{\mathrm{2}} }}{dx}=\frac{\pi}{\mathrm{4}}{ln}\mathrm{3} \\ $$ Answered by Ñï= last updated on 24/Mar/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}}…

The-result-log-xy-log-x-log-y-is-not-always-true-Give-a-pair-of-values-of-x-and-y-such-that-the-result-will-not-hold-

Question Number 5569 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{The}\:\mathrm{result}\:“\mathrm{log}\:\mathrm{xy}=\mathrm{log}\:\mathrm{x}+\mathrm{log}\:\mathrm{y}''\:\mathrm{is}\:\mathrm{not} \\ $$$$\mathrm{always}\:\mathrm{true}!\:\mathrm{Give}\:\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of} \\ $$$$\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{will}\:\mathrm{not}\:\mathrm{hold}. \\ $$ Commented by Yozzii last updated on 20/May/16 $$\left({x},{y}\right)=\left(−\mathrm{1},\mathrm{2}\right)…

Question-71096

Question Number 71096 by Omer Alattas last updated on 11/Oct/19 Answered by $@ty@m123 last updated on 11/Oct/19 $${Let}\:{x}=\mathrm{1}+{y} \\ $$$$\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\:\frac{{y}}{\mathrm{ln}\:\left(\mathrm{1}+{y}\right)} \\ $$$$\:\:\frac{\mathrm{1}}{\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+{y}\right)}{{y}}}=\mathrm{1} \\…

A-chord-is-drawn-in-a-circle-that-divides-the-circle-in-1-2-ratio-In-what-ratio-the-chord-divides-the-diameter-perpendicular-to-the-chord-

Question Number 5561 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{A}\:\mathrm{chord}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{that} \\ $$$$\mathrm{divides}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{in}\:\mathrm{1}:\mathrm{2}\:\left(\mathrm{ratio}\right). \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{ratio}\:\mathrm{the}\:\mathrm{chord}\:\mathrm{divides} \\ $$$$\mathrm{the}\:\mathrm{diameter}\:\mathrm{perpendicular}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{chord}? \\ $$ Commented by Rasheed Soomro…

The-area-of-a-circle-is-diretly-proportional-to-the-square-of-its-diameter-What-is-the-constant-of-proportionality-

Question Number 5556 by Rasheed Soomro last updated on 20/May/16 $$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{diretly}\: \\ $$$$\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{diameter}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{proportionality}? \\ $$ Commented by Yozzii last updated on…

Question-71091

Question Number 71091 by Henri Boucatchou last updated on 11/Oct/19 Commented by Prithwish sen last updated on 11/Oct/19 $$\boldsymbol{\mathrm{It}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{as}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \sqrt{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\mathrm{1}}\:\boldsymbol{\mathrm{dx}}\:−\int_{\mathrm{0}}…

nice-calculus-suppose-that-p-0-ln-1-x-p-x-2-find-the-value-of-1-0-p-1-p-dp-

Question Number 136626 by mnjuly1970 last updated on 24/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……….{nice}\:\:\:\:{calculus}……… \\ $$$$\:\:\:\:{suppose}\:{that}::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\varphi\left({p}\right)=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}\right)}{\left({p}+{x}\right)^{\mathrm{2}} }\:…\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{1}} \:\frac{\varphi\left({p}\right)}{\mathrm{1}+{p}}{dp}=?… \\ $$$$\:\:\:\:\:\:…