Category: Integration

Question Number 146147 by iloveisrael last updated on 11/Jul/21 $$\mathrm{{\rm Y}}=\int \frac{\mathrm{dx}}{{\mathrm{x}}^4\sqrt{{\mathrm{x}}^2-{\mathrm{a}}^2}}=?$$ Answered by EDWIN88 last updated on 11/Jul/21 $$\:{Solve}\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} \:\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}}…

Question Number 15045 by Tinkutara last updated on 07/Jun/17 $$\mathrm{In}\mathrm{a}\mathrm{curve}\mathrm{the}x\mathrm{and}y\mathrm{co}-\mathrm{ordinate}\mathrm{is}$$$$\mathrm{function}\mathrm{of}t\mathrm{is}\mathrm{given}\mathrm{by}\mathrm{the}\mathrm{equation}$$$$x=\cos t\mathrm{and}y=\sin t,\mathrm{then}\mathrm{find}\mathrm{the}$$$$\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{curve}\mathrm{for}t=0\mathrm{to}t=\frac{\pi }{2}.$$ Answered by mrW1 last updated on 07/Jun/17…

Question Number 146110 by puissant last updated on 11/Jul/21 $$\int \frac{\mathrm{x}+1}{{2\mathrm{x}}^2+\mathrm{x}+1}\mathrm{dx}$$ Answered by gsk2684 last updated on 11/Jul/21 $$\int \frac{\frac{1}{4}(4x+1)-\frac{1}{4}+1}{2x^2+x+1}dx$$$$\frac{\mathrm{1}}{\mathrm{4}}\mathrm{log}\:\mid\mathrm{2}{x}^{\mathrm{2}} +{x}+\mathrm{1}\mid+\frac{\mathrm{3}}{\mathrm{4}}\int\frac{\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}}…

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}}…