Question Number 59667 by tanmay last updated on 13/May/19
Answered by tanmay last updated on 13/May/19
![∫_a ^b f(x)dx=∫_a ^b f(a+b−x)dx I=∫_4 ^(10) (([x^2 ])/([(x−14)^2 ]+[x^2 ]))dx I=∫_4 ^(10) (([(14−x)^2 ])/([x^2 ]+[(14−x)^2 ]))dx 2I=∫_4 ^(10) dx I=3](https://www.tinkutara.com/question/Q59686.png)
$$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}=\int_{{a}} ^{{b}} {f}\left({a}+{b}−{x}\right){dx} \\ $$$${I}=\int_{\mathrm{4}} ^{\mathrm{10}} \frac{\left[{x}^{\mathrm{2}} \right]}{\left[\left({x}−\mathrm{14}\right)^{\mathrm{2}} \right]+\left[{x}^{\mathrm{2}} \right]}{dx} \\ $$$${I}=\int_{\mathrm{4}} ^{\mathrm{10}} \frac{\left[\left(\mathrm{14}−{x}\right)^{\mathrm{2}} \right]}{\left[{x}^{\mathrm{2}} \right]+\left[\left(\mathrm{14}−{x}\right)^{\mathrm{2}} \right]}{dx} \\ $$$$\mathrm{2}{I}=\int_{\mathrm{4}} ^{\mathrm{10}} {dx} \\ $$$${I}=\mathrm{3} \\ $$