How Does FTC1 Help in Finding the Derivative of G(x)?

[aeonsky]

I need to find the derivative of the function below...

Homework Statement

G(x) = \int_{x}^{1} cos(\sqrt{t}) dt

Homework Equations

FTC1

If f is continuous on [a,b], then the function g defined by

g(x) = \int_{a}^{x} f(t) dt a \leq x \leq b

is continuous on [a,b] and differentiable on (a,b) and g'(x) = f(x)

The Attempt at a Solution

Would it be -cos(sqrt(t))

Thanks for the time!

 

[HallsofIvy]

It would be -cos(\sqrt{x}), not t.

 

[lurflurf]

First you might reverse the limits, which reveses the sighn. FTC1 says the derivative of the integral of a function is the function. Differendiation cancels integration.