# Thread: Second Fundamental Theorem of Calculus!!

1. ## Second Fundamental Theorem of Calculus!!

Find the derivative.

i need help finding this, i dont know how to do it, thanks

2. Generally, you notice that the Derivative and the Integral are very closely related and you simply write down the answer.

Think about $(1+x)^{900}$

3. Hello,

Let F be an antiderivative of f.

Then, $\int_a^b f(t)dt=F(b)-F(a)$

According to it, what can you say ?

4. In a nutshell. The second fundamental theorem of Calculus states:

$\frac d{dx} \int_c^x f(t)~dt = f(x)$

where $c$ is a constant

More generally (By the chain rule), $\frac d{dx} \int_c^{g(x)}f(t)~dt = f(g(x)) \cdot g'(x)$

5. Originally Posted by Jhevon
In a nutshell. The second fundamental theorem of Calculus states:

$\frac d{dx} \int_c^x f(t)~dt = f(x)$

where $c$ is a constant

More generally (By the chain rule), $\frac d{dx} \int_c^{g(x)}f(t)~dt = f(g(x)) \cdot g'(x)$
you're just gonna have to show me how to do it please, then i'll be able to understand better thanks

6. Originally Posted by mathlete
you're just gonna have to show me how to do it please, then i'll be able to understand better thanks
you have the first case (c = 1), do you see that? your f(t) is $(1 + t)^{900}$, so your answer should be f(x). what would f(x) be?