Calculate F'(x)

• Jan 12th 2010, 05:04 PM
450081592
Calculate F'(x)
F(x) = $\int _1\,^x\!$ $sin\pi t$ dt

I know that F'(x) = f(x), but what is f(x) here? do I just sub x into $sin\pi t$?
• Jan 12th 2010, 05:06 PM
Krizalid
Your writting is quite hard to read, better you to improve it.

Besides, it's a simple application of the FTC.
• Jan 12th 2010, 05:23 PM
skeeter
Quote:

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

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

fixed latex ...

yes ...

if $F(x) = \int_a^x f(t) \, dt$ , then $F'(x) = f(x)$
• Jan 12th 2010, 05:29 PM
450081592
Quote:

Originally Posted by skeeter
yes ...

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

Ya Ibut where is f(x) here? is it $sin\pi x$ ?
• Jan 12th 2010, 06:17 PM
mr fantastic
Quote:

Originally Posted by 450081592
Ya Ibut where is f(x) here? is it $sin\pi x$ ?

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)?