Category: Integration

Question Number 214750 by universe last updated on 18/Dec/24 Answered by aleks041103 last updated on 21/Dec/24 $${J}=\int_{\mathrm{0}} ^{\infty} \int_{{z}} ^{\infty} \int_{{z}} ^{\infty} {cos}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right){dxdydz}…

Question Number 214661 by efronzo1 last updated on 15/Dec/24 Answered by Rasheed.Sindhi last updated on 15/Dec/24 $$x.f\left(x\right)+x.f\left(\frac{1}{x}\right)=x+1$$$$f\left(x\right)+f\left(\frac{1}{x}\right)=\frac{x+1}{x}\dots \dots A$$$$Replacexby\frac{1}{x}:$$$$f\left(\frac{1}{x}\right)+f\left(x\right)=\frac{\frac{1}{x}+1}{\frac{1}{x}}=x+1\dots B$$$${A}\:\&\:{B}:\:\:\:\frac{{x}+\mathrm{1}}{{x}}={x}+\mathrm{1}…

Question Number 214568 by Ikbal last updated on 12/Dec/24 $$\int \frac{b+ax}{1+\sin x}dx$$ Answered by MathematicalUser2357 last updated on 18/Dec/24 $$\int \frac{ax+b}{\sin x+1}dx$$$$=\int \frac{(ax+b)\sec x}{\tan x+\sec x}dx$$$$=−\frac{{ax}+{b}}{\mathrm{tan}\:{x}+\mathrm{sec}\:{x}}+\int\frac{{a}}{\mathrm{tan}\:{x}+\mathrm{sec}\:{x}}{dx} \…

Question Number 214509 by depressiveshrek last updated on 10/Dec/24 $$\mathrm{Find}\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{of}\mathrm{revolution}$$$$\mathrm{generated}\mathrm{by}\mathrm{rotating}\mathrm{the}\mathrm{area}\mathrm{bounded}$$$$\mathrm{by}y=x(2-x)\mathrm{and}y=x\mathrm{about}\mathrm{the}\mathrm{y}-\mathrm{axis}.$$ Commented by mr W last updated on 11/Dec/24 $${you}\:{seem}\:{never}\:{to}\:{give}\:{any}\:{feedback}…

Question Number 214360 by shunmisaki007 last updated on 06/Dec/24 $$\mathrm{Find}\underset{-\mathrm{\infty }}{\stackrel{\mathrm{\infty }}{\int }}{e}^{-{ax}^2}dx\mathrm{when}a\mathrm{is}\mathrm{constant}\mathrm{without}\mathrm{changing}\mathrm{the}\mathrm{coordinate}.$$ Answered by mathmax last updated on 06/Dec/24 $$=\mathrm{2}\int_{\mathrm{0}} ^{\infty}…