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 50689 by Tawa1 last updated on 18/Dec/18

$$\mathrm{If}\mathrm{c}\mathrm{is}\mathrm{the}\mathrm{line}\mathrm{segement}\mathrm{from}(0,0,0)\mathrm{to}(1,2,3)$$$$\mathrm{find}\int \mathrm{x}{\mathrm{e}}^{\mathrm{yz}}\mathrm{ds}$$

Answered by mr W last updated on 19/Dec/18

$$\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$$$$\Rightarrow y=2x$$$$\Rightarrow z=3x$$$$ds=\sqrt{{\left(dx\right)}^2+{\left(dy\right)}^2+{\left(dz\right)}^2}=\sqrt{1+2^2+3^2}dx=\sqrt{14}dx$$$$\int {xe}^{yz}ds={\int }_0^1{xe}^{6x^2}\sqrt{14}dx$$$$=\frac{\sqrt{14}}{12}{\int }_0^1{e}^{6x^2}d\left(6x^2\right)$$$$=\frac{\sqrt{14}}{12}{\left[e^{6x^2}\right]}_0^1$$$$=\frac{\sqrt{14}}{12}(e^6-1)$$

Commented by Tawa1 last updated on 19/Dec/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com