Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 84456 by M±th+et£s last updated on 13/Mar/20

$$y=ln\sqrt{\frac{a+sin\left(x\right)}{b-sin\left(x\right)}}$$$$if{\left(\frac{dy}{dx}\right)}^2-{tan}^2\left(x\right)=1$$$$showthata=b$$

Commented by jagoll last updated on 13/Mar/20

$${\mathrm{e}}^{2\mathrm{y}}=\frac{\sin \mathrm{x}+\mathrm{a}}{-\sin \mathrm{x}+\mathrm{b}}$$$${2\mathrm{e}}^{2\mathrm{y}}{\mathrm{y}}^{\prime }=\frac{(\mathrm{b}+\mathrm{a})\cos \mathrm{x}}{{(-\sin \mathrm{x}+\mathrm{b})}^2}$$$${4\mathrm{e}}^{2\mathrm{y}}{\mathrm{y}}^{\prime }+{2\mathrm{e}}^{2\mathrm{y}}{\mathrm{y}}^{″}=\frac{(\mathrm{a}+\mathrm{b})\sin \mathrm{x}{(\mathrm{b}-\sin \mathrm{x})}^2+2(\mathrm{a}+\mathrm{b})\cos {}^2\mathrm{x}(\mathrm{b}-\sin \mathrm{x})}{{(\mathrm{b}-\sin \mathrm{x})}^4}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com