Category: Integration

Question Number 186911 by Spillover last updated on 11/Feb/23 $$$$$${\int }_0^{\mathrm{\infty }}\frac{1}{1+a^x+a^{\frac{x}{2}}}dx=\frac{1}{\ln a}[\ln 3-\frac{\pi }{3\sqrt{3}}]$$ Answered by witcher3 last updated on 13/Feb/23…

Question Number 55834 by Tawa1 last updated on 04/Mar/19 Answered by ajfour last updated on 04/Mar/19 $$(2-1)f_{min}(x=2)⩽{\int }_1^{2}f\left(x\right)dx⩽\frac{(2-1)}{2}[f\left(1\right)+f\left(2\right)]$$$$\:\:\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{17}}\:\leqslant\int_{\mathrm{1}} ^{\:\:\mathrm{2}} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} }\:\leqslant\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{17}}\right)\:<\:\frac{\mathrm{7}}{\mathrm{24}}\:.…

Question Number 121314 by Bird last updated on 06/Nov/20 $$find{lim}_{n\to +\mathrm{\infty }}{\int }_0^n\frac{cos\left(nx\right)}{x^2+n^2}dx$$ Answered by mathmax by abdo last updated on…

Question Number 186840 by cortano12 last updated on 11/Feb/23 $$\underset{9}{\stackrel{16}{\int }}\frac{\sqrt{4-\sqrt{x}}}{x}dx=?$$ Answered by horsebrand11 last updated on 11/Feb/23 $$\:\:{I}=\underset{\mathrm{9}} {\overset{\:\mathrm{16}} {\int}}\:\frac{\sqrt{\mathrm{4}−\sqrt{{x}}}}{{x}}\:{dx}\:=? \…

Question Number 55759 by maxmathsup by imad last updated on 03/Mar/19 $$calculateI={\int }_0^{2\pi }\frac{cost}{3+sin\left(2t\right)}dtandJ={\int }_0^{2\pi }\frac{sint}{3+cos\left(2t\right)}dt.$$ Answered by MJS last updated on 04/Mar/19…