Category: Integration

Question Number 215344 by universe last updated on 03/Jan/25 Answered by MrGaster last updated on 04/Jan/25 $$\mathrm{Let}\mathrm{\Sigma }\mathrm{be}\mathrm{the}\mathrm{boundary}\mathrm{of}D.$$$$\mathrm{\Sigma }=\sum _1\cup \sum _2\cup \sum _3$$$$\mathrm{where}$$$$\sum_{\mathrm{1}}…

Question Number 215315 by depressiveshrek last updated on 02/Jan/25 $$\mathrm{Evaluate}\underset{n\to \mathrm{\infty }}{\lim }(\frac{1}{2n+1}+\frac{1}{2n+2}+\dots +\frac{1}{4n})$$ Answered by mr W last updated on 02/Jan/25 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{n}+{k}}…

Question Number 215188 by MrGaster last updated on 31/Dec/24 $${\int }_0^{\mathrm{\infty }}\frac{x\cos 2\pi x}{e^{2\pi \sqrt{x}}-1}dx$$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\approx 0.000807442$$…

Question Number 215185 by MrGaster last updated on 31/Dec/24 $${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\frac{\exp \left(\frac{ax}{1+x^2}\right)\exp \left(\frac{a}{1+x^2}\right)}{1+x^2}dx,a>0$$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\mathrm{Oops}!\:\mathrm{Make}\:\mathrm{sure}\:\mathrm{you}\:\mathrm{typed}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{made}\:\mathrm{of}\:{x}.…

Question Number 215187 by MrGaster last updated on 31/Dec/24 $${\int }_0^1\frac{x{\mathit{K}}^2\left(x\right)}{\sqrt{1-x^2}}dx$$ Answered by MathematicalUser2357 last updated on 31/Dec/24 $$\approx\mathrm{8}.\mathrm{473967} \…