Category: Integration

Question Number 187164 by mathlove last updated on 14/Feb/23 Answered by qaz last updated on 14/Feb/23 $$\underset{p\to ln\frac{1}{2}}{lim}\frac{ln2+ln2cosp}{{\left(cosln\frac{1}{\sqrt{2}}\right)}^2}=\frac{(1+cosln2)ln2}{cos{}^2\frac{1}{2}ln2}=\frac{\left[2\cos {}^2\frac{1}{2}ln2\right]ln2}{{cos}^2\frac{1}{2}ln2}=2ln2$$$$\underset{{p}=\mathrm{0}} {\overset{\infty}…

Question Number 121602 by benjo_mathlover last updated on 09/Nov/20 Answered by liberty last updated on 10/Nov/20 $$\mathrm{I}=\underset{0}{\stackrel{\pi /2}{\int }}\frac{\mathrm{dx}}{{\mathrm{b}}^2\tan {}^2\mathrm{x}+1}$$$$\mathrm{let}\:\phi=\mathrm{b}\:\mathrm{tan}\:\mathrm{x}\:\Rightarrow\mathrm{d}\phi=\mathrm{bsec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}\: \…

Question Number 187135 by cortano12 last updated on 14/Feb/23 $$\underset{0}{\stackrel{\pi /4}{\int }}\frac{\tan {}^{2}x}{1+\sin x}dx=?$$ Answered by horsebrand11 last updated on 14/Feb/23 $$\:{I}=\underset{\:\mathrm{0}} {\overset{\:\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{tan}\:^{\mathrm{2}}…

Question Number 56061 by necx1 last updated on 09/Mar/19 $${\int }_0^1{e}^{-x^2}dxcorrectto3decimalplace.$$ Answered by tanmay.chaudhury50@gmail.com last updated on 09/Mar/19 $$\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 121548 by benjo_mathlover last updated on 09/Nov/20 $$\underset{0}{\stackrel{\pi /4}{\int }}\tan {}^6\mathrm{x}\sec \mathrm{x}\mathrm{dx}=?$$ Answered by MJS_new last updated on 09/Nov/20 $$\int\mathrm{tan}^{\mathrm{6}} \:{x}\:\mathrm{sec}\:{x}\:{dx}=\int\frac{\mathrm{sin}^{\mathrm{6}} \:{x}}{\mathrm{cos}^{\mathrm{7}}…