## Study23 Group Title Help with Part 1 of the Fundamental Theorem of Calculus?? What does this mean? (d/dx) integral x to a f(t) dt = f(x)?????? one year ago one year ago

1. satellite73

it means, in english, that "the derivative of the integral is the integrand"

2. Study23

I'm confused about the d/dx part in particular...

3. satellite73

that is, if $F(x)=\int_a^xf(t)dt$ then $F'(x)=f(x)$

4. satellite73

notice that $F(x)=\int_a^xf(t)dt$ is a function of the variable $$x$$ and not of $$t$$

5. satellite73

for example, if $F(x)=\int_0^x\sin(t)dt$ then $F'(x)=\sin(x)$

6. Study23

So what does that mean d/dx mean exactly? Does it have todo with the dx dummy variable? Sorry, but that d/dx I throwing me off. Does it mean I have to take the derivative once I find the anti derivative?

7. satellite73

the $$\frac{d}{dx}$$ notation just means the derivative wrt $$x$$ do not be confused by that, it is the same as saying the derivative of the integral is the integrand