Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 77347 by key of knowledge last updated on 05/Jan/20

$$\mathrm{if}\int \sin \left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=\mathrm{g}\left(\mathrm{x}\right)$$$$\int \cos \left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=?$$

Commented by mind is power last updated on 05/Jan/20

$$\mathrm{non}\mathrm{close}\mathrm{forme}\mathrm{answer}\mathrm{depend}\mathrm{in}\mathrm{functio}\mathrm{f}$$$$$$

Answered by Henri Boucatchou last updated on 06/Jan/20

$$\int \mathit{c}\mathit{o}\mathit{s}\left(\mathit{f}\left(\mathit{x}\right)\right)\mathit{d}\mathit{x}=\int g^{″}\left(x\right)dx={\mathit{g}}^{\prime }\left(\mathit{x}\right)+\mathit{C}\mathit{t}\mathit{e}$$

Commented by mr W last updated on 06/Jan/20

$${it}^{\prime }swrongsir.$$$$\sin \left(f\left(x\right)\right)=g^{\prime }\left(x\right)$$$$\cos \left(f\left(x\right)\right)\times f{}^{\prime }\left(x\right)=g^{″}\left(x\right)$$$$\Rightarrow \cos \left(f\left(x\right)\right)=\frac{g^{″}\left(x\right)}{f{}^{\prime }\left(x\right)}\ne g^{\prime }\left(x\right)$$

Answered by john santu last updated on 06/Jan/20

$$\sin \left(\mathrm{f}\left(\mathrm{x}\right)\right)={\mathrm{g}}^{\prime }\left(\mathrm{x}\right)$$$$\cos \left(\mathrm{f}\left(\mathrm{x}\right)\right)=\sqrt{1-\sin {}^2\left(\mathrm{f}\left(\mathrm{x}\right)\right)}$$$$\cos \left(\mathrm{f}\left(\mathrm{x}\right)\right)=\sqrt{1-{\left({\mathrm{g}}^{\prime }\left(\mathrm{x}\right)\right)}^2}$$$$\mathrm{let}{\mathrm{g}}^{\prime }\left(\mathrm{x}\right)=\mathrm{u}\Rightarrow \int \cos \left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}$$$$=\int \sqrt{1-{\mathrm{u}}^2}\left(\frac{\mathrm{du}}{{\mathrm{u}}^{\prime }}\right)$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com