Category: Integration

Question Number 15036 by Tinkutara last updated on 07/Jun/17 $$\mathrm{Rotating}\mathrm{a}\mathrm{curve}y=\sqrt{x}\mathrm{about}\mathrm{the}x-$$$$\mathrm{axis}\mathrm{produces}\mathrm{a}“\mathrm{head}{\mathrm{light}}^{″}\mathrm{as}\mathrm{shown}$$$$\mathrm{below}.$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{disc}\mathrm{at}\mathrm{any}x?$$ Commented by Tinkutara last updated on 07/Jun/17…

Question Number 146090 by Ar Brandon last updated on 10/Jul/21 $${\int }_0^{\mathrm{\infty }}\frac{\sinh \left(\mathrm{at}\right)\sinh \left(\mathrm{bt}\right)}{\sinh \left(\mathrm{ct}\right){\mathrm{e}}^{\mathrm{tz}}}\mathrm{dt}=$$$$\frac{\mathrm{ab}}{\mathrm{c}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} +\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\mathrm{K}}}\frac{−\mathrm{4k}^{\mathrm{2}} \left(\mathrm{k}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}}…

Question Number 146067 by gsk2684 last updated on 10/Jul/21 $$transformthecartesianinyegral$$$$\underset{0}{\stackrel{1}{\int }}\underset{0}{\stackrel{\sqrt{1-x^2}}{\int }}{e}^{-(x^2+y^2)}dydxintopolarintegral$$$$andevaluateit.$$ Answered…

Question Number 146035 by KONE last updated on 10/Jul/21 $$helpmeplease$$$$\int \frac{ln(x+1)}{x}dx=??$$$$$$ Answered by KONE last updated on 10/Jul/21 $${please} \…

Question Number 80452 by abdomathmax last updated on 03/Feb/20 $$find{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{cos(2x^2+1)}{x^4-x^2+3}dx$$ Commented by abdomathmax last updated on 03/Mar/20 $${I}=\:{Re}\left(\int_{−\infty}…