Question

If f is the function given by f(x)= integral from (4 to 2x) of sqrt(t^2-t)dt then f'(2) =?

Answer 1

The question ask to calculate the function f'(2) in the F is the function given by f(x) = integral from (4 to 2x) of sqrt(t^2-t), base on that, the possible answer would be that the f(2) is 4 sqrt 3. I hope you are satisfied with my answer and feel free to ask for more if you have questions 

Answer 2

Hello,

$f(x)= \int\limits^{2x}_4 {\sqrt{t^2-t} \, dt \\ \dfrac{df(x)}{dx} = \dfrac{df(x)}{d(2x)} * \dfrac{d(2x)}{dx} =2* \sqrt{(2x)^2-2x} \\ f'(2)=2 * \sqrt{4^2-4} =2* \sqrt{12} =4 \sqrt{3}$