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Category: Integration

0-1-cos-4x-xe-x-dx-

Question Number 157750 by cortano last updated on 27/Oct/21 $$\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−\mathrm{cos}\:\mathrm{4}{x}}{{xe}^{{x}} }\:{dx}=? \\ $$ Answered by qaz last updated on 27/Oct/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−\mathrm{cos}\:\mathrm{4x}}{\mathrm{xe}^{\mathrm{x}}…

let-a-b-c-be-three-digits-all-different-of-zero-Prove-that-ac-cb-a-b-n-1-accc-cc-ccc-ccb-a-b-the-number-accc-cc-has-the-digit-c-n-times-

Question Number 92188 by ~blr237~ last updated on 05/May/20 $${let}\:{a},{b},{c}\:{be}\:{three}\:{digits}\:{all}\:{different}\:{of}\:{zero} \\ $$$${Prove}\:{that}\:\frac{{ac}}{{cb}}=\frac{{a}}{{b}}\:\Leftrightarrow\:\forall\:{n}\geqslant\mathrm{1}\:\:\:\:\frac{{accc}…{cc}}{{ccc}…{ccb}}\:=\frac{{a}}{{b}}\:\:\: \\ $$$${the}\:{number}\:{accc}…{cc}\:\:\:{has}\:{the}\:{digit}\:{c}\:\:{n}\:{times} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-26626

Question Number 26626 by ajfour last updated on 27/Dec/17 Answered by mrW1 last updated on 28/Dec/17 $${let}'{s}\:{take}\:{point}\:{V}\:{as}\:{origin}\:{and}\:{VC} \\ $$$${as}\:{x}−{axis},\:{then} \\ $$$${C}\left({r},\:\mathrm{0}\right) \\ $$$${P}\left({r},{r}\right) \\ $$$${Eqn}.\:{of}\:{red}\:{parabola}\:{is}\:…