1. ## Calculate F'(x)

F(x) = $\displaystyle \int _1\,^x\!$ $\displaystyle sin\pi t$ dt

I know that F'(x) = f(x), but what is f(x) here? do I just sub x into $\displaystyle sin\pi t$?

2. Your writting is quite hard to read, better you to improve it.

Besides, it's a simple application of the FTC.

3. Originally Posted by 450081592
$\displaystyle F(x) = \int _1^x \sin{\pi t} \, dt$

I know that $\displaystyle F'(x) = f(x)$, but what is $\displaystyle f(x)$ here? do I just sub x into $\displaystyle \sin{\pi t}$?

fixed latex ...
yes ...

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

4. Originally Posted by skeeter
yes ...

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

Ya Ibut where is f(x) here? is it $\displaystyle sin\pi x$ ?

5. Originally Posted by 450081592
Ya Ibut where is f(x) here? is it $\displaystyle sin\pi x$ ?
Please read post #3 again. Do you see what f(t) is? Do you know how to replace t with x to get f(x)?