Integral calculus help please. How do you use the FTC (part 1) when both a and b have x?

Question

anonymous · Answer

you would just use it as you normally would

anonymous · Answer

treat those values as a and b

anonymous · Answer

The first fundamental theorem of calculus?

hartnn · Answer

you need to find the derivative of that integral ?

anonymous · Answer

That was my next question

hartnn · Answer

$\Large \dfrac{d}{dx}\int \limits_{f(x)}^{g(x)}h(x)dx = H(g(x))g'(x)-H(f(x))f'(x)$

hartnn · Answer

basically you will need to use the chain rule

hartnn · Answer

since here g(x) = x
g'(x) = 1 only

hartnn · Answer

but f(x) is a function of x,
so you need to find f'(x)
f(x) = sqrt x

hartnn · Answer

did u get what to do ?

hartnn · Answer

good, if you want me to verify your final answer, tell us what u got :)

anonymous · Answer

would it not be $h(g(x))g'(x)-h(f(x))f'(x)$? with capital H it just makes me think it's an anti-derivative

hartnn · Answer

^ thats correct
sorry for the confusion