Question

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

Answer 1

you would just use it as you normally would

Answer 2

treat those values as a and b

Answer 3

The first fundamental theorem of calculus?

Answer 4

you need to find the derivative of that integral ?

Answer 5

That was my next question

Answer 6

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

Answer 7

basically you will need to use the chain rule

Answer 8

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

Answer 9

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

Answer 10

did u get what to do ?

Answer 11

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

Answer 12

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

Answer 13

^ thats correct
sorry for the confusion