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Category: Integration

Show-that-the-function-x-x-3-is-of-Riemann-within-the-interval-1-2-then-calculate-1-2-x-2-dx-

Question Number 92799 by Ar Brandon last updated on 09/May/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{x}\rightarrow\mathrm{x}^{\mathrm{3}} \:\mathrm{is} \\ $$$$\mathrm{of}\:\mathrm{Riemann}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[−\mathrm{1},\mathrm{2}\right] \\ $$$$\mathrm{then}\:\mathrm{calculate}\:\int_{−\mathrm{1}} ^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} \mathrm{dx} \\ $$ Commented by mathmax by…

Define-Clairaut-s-equation-and-solve-y-px-a-2-p-2-b-2-

Question Number 92795 by niroj last updated on 09/May/20 $$\boldsymbol{\mathrm{Define}}\:\boldsymbol{\mathrm{Clairaut}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{solve}} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{y}}=\:\boldsymbol{\mathrm{px}}\:+\sqrt{\boldsymbol{\mathrm{a}}^{\mathrm{2}} \boldsymbol{\mathrm{p}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

prove-that-n-1-H-n-F-n-2-n-ln-4-12-5-ln-Golden-ratio-F-n-fibonacci-numbers-

Question Number 158320 by mnjuly1970 last updated on 02/Nov/21 $$ \\ $$$$\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{H}_{\:{n}} .\:\mathrm{F}_{{n}} }{\mathrm{2}^{\:{n}} }\:\:=\:{ln}\left(\mathrm{4}\right)\:+\:\frac{\mathrm{12}}{\:\sqrt{\mathrm{5}}}\:{ln}\left(\:\varphi\:\right) \\ $$$$\:\:\:\:\:\varphi\::\:\:\:\mathrm{Golden}\:\:\mathrm{ratio} \\ $$$$\:\:\:\:\:\:\mathrm{F}_{\:{n}}…

Question-92772

Question Number 92772 by Power last updated on 09/May/20 Commented by mathmax by abdo last updated on 09/May/20 $${A}\:=\int_{\mathrm{0}} ^{\mathrm{6}} \:\left[{x}\right]\:{sin}\left(\frac{\pi{x}}{\mathrm{6}}\right){dx}\:\Rightarrow\:{A}\:=\sum_{{k}=\mathrm{0}} ^{\mathrm{5}} \:\int_{{k}} ^{{k}+\mathrm{1}} \:{k}\:{sin}\left(\frac{\pi{x}}{\mathrm{6}}\right){dx}…

Question-158288

Question Number 158288 by cortano last updated on 02/Nov/21 Answered by mr W last updated on 02/Nov/21 $${y}_{\mathrm{1}} −{y}_{\mathrm{2}} ={ax}^{\mathrm{2}} −{ax}−\mathrm{2}{a}={a}\left({x}^{\mathrm{2}} −{x}−\mathrm{2}\right) \\ $$$$\Delta={a}^{\mathrm{2}} +\mathrm{8}{a}^{\mathrm{2}}…