Category: Integration

Question Number 39440 by rahul 19 last updated on 06/Jul/18 $$\mathrm{f}\left(x\right)={\int }_0^{x_{}}{e}^t\left(\frac{1+\sin t}{1+\cos t}\right)dt.$$$$T\mathrm{hen}\mathrm{f}\left(\frac{\pi }{3}\right)\times \mathrm{f}\left(\frac{2\pi }{3}\right)=?$$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 170501 by kndramaths last updated on 25/May/22 $$solvethis:$$$$\int {\int }_D{x}^2{e}^{xy}dxdy$$$$D:\{(x.y)\in R^2/0⩽x⩽1.0⩽y⩽2\}$$$$\:\:\:\:\:\:\int\underset{{D}} {\int}\frac{{ydxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }.\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}.\mathrm{0}\leqslant{y}\leqslant\mathrm{1}. \…

Question Number 170475 by mnjuly1970 last updated on 24/May/22 $$$$$$AneasyquestionofMeasuretheory:$$$$$$$$Provethat:\mu \left(\mathrm{Q}\right)=0\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fc.svg">}m.n$$$$$$ Terms of Service Privacy Policy…

Question Number 39389 by maxmathsup by imad last updated on 05/Jul/18 $$calculateF\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{dt}{1+{(1+x(1+t^2))}^2}$$ Commented by prof Abdo imad last updated…

Question Number 39384 by rahul 19 last updated on 05/Jul/18 $$\mathrm{The}\mathrm{values}\mathrm{of}\mathrm{a}\mathrm{for}\mathrm{which}\mathrm{y}=\mathrm{a}{x}^2+ax+\frac{1}{24}$$$$andx={ay}^2+ay+\frac{1}{24}toucheachother$$$$are$$$$1)\frac{2}{3}2)\frac{3}{2}$$$$3)\frac{13+\sqrt{601}}{12}4)\frac{13-\sqrt{601}}{12}.$$ Answered by…