Category: Integration

Question Number 158839 by EbrimaDanjo last updated on 09/Nov/21 $$\mathrm{Evaluate}\mathrm{the}\mathrm{following}\mathrm{integrals}\mathrm{using}$$$$\mathrm{integration}\mathbf{By}\mathbf{Parts}$$$$1.{\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}{xcsc}^{2}xdx$$$$$$$$2.{\int }_1^{\sqrt{3}}arctan\left(\frac{1}{x}\right)dx$$…

Question Number 158822 by qaz last updated on 09/Nov/21 $$\underset{\mathrm{n}=0}{\sum ^{\mathrm{\infty }}}\arctan \frac{{(-1)}^{\mathrm{n}}}{2\mathrm{n}+1}=?$$ Answered by mindispower last updated on 09/Nov/21 $$\underset{{n}\geqslant\mathrm{0}} {\sum}\left\{{arctan}\left(\frac{\mathrm{1}}{\mathrm{4}{n}+\mathrm{1}}\right)−{arctan}\left(\frac{\mathrm{1}}{\mathrm{4}{n}+\mathrm{3}}\right)\right\} \…

Question Number 93248 by i jagooll last updated on 12/May/20 $$\int \underset{0}{\stackrel{1}{}}\ln \left(\mathrm{x}\right)\mathrm{dx}$$ Commented by abdomathmax last updated on 12/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){dx}\:={lim}_{{a}\rightarrow\mathrm{0}^{+}…

Question Number 27692 by abdo imad last updated on 12/Jan/18 $$findbytwowaysthevalueof\int {\int }_{[0,1]}{x}^{y}dxdxythen$$$$calculate{\int }_0^1\frac{t-1}{lnt}dt.$$ Commented by abdo imad last updated…

Question Number 93225 by Ajao yinka last updated on 11/May/20 Commented by prakash jain last updated on 12/May/20 $$1+x+\dots +x^n\mathrm{has}\mathrm{no}\mathrm{root}\mathrm{in}\mathbb{R}\mathrm{for}n\mathrm{even}$$$$\int_{−\infty} ^{\infty} {x}^{{n}} \delta\left(\mathrm{1}+{x}+…+{x}^{{n}}…