# Math Help - Fundamentals of Calc

1. ## Fundamentals of Calc

Let G(x) be the integral of f(t)=sin(t) over the interval [0, x], x>0. Which of the following is G'(x), the derivative of G(x) with respect to x?

cos (x)
cos (t)
sin (x)
sin (t)

2. Originally Posted by Billy Maize
Let G(x) be the integral of f(t)=sin(t) over the interval [0, x], x>0. Which of the following is G'(x), the derivative of G(x) with respect to x?

cos (x)
cos (t)
sin (x)
sin (t)
sin(x)

3. Amer is correct. In general:

$\frac{d}{dx} \left[ \int_a^u f(t) dt\right] = f(u) \cdot \frac{du}{dx}
$