Question Number 535 by kth last updated on 25/Jan/15
$$\int_{\mathrm{4}} ^{\mathrm{1}} \frac{\mathrm{2}}{\:\sqrt{{x}}} \\ $$
Answered by 13/NaSaNa(N)056565 last updated on 25/Jan/15
![=2∫_4 ^1 x^((−1)/2) dx =2[2x^(1/2) ]_4 ^1 =4[(√x)]_4 ^1 =4[1−2] =−4](https://www.tinkutara.com/question/Q541.png)
$$=\mathrm{2}\int_{\mathrm{4}} ^{\mathrm{1}} {x}^{\frac{−\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$=\mathrm{2}\left[\mathrm{2}{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \right]_{\mathrm{4}} ^{\mathrm{1}} \\ $$$$=\mathrm{4}\left[\sqrt{{x}}\right]_{\mathrm{4}} ^{\mathrm{1}} \\ $$$$=\mathrm{4}\left[\mathrm{1}−\mathrm{2}\right] \\ $$$$=−\mathrm{4} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$