# Integration

• Aug 11th 2010, 07:16 PM
blackdragon190
Integration
I'm stuck with this problem - I can barely even understand what it says!

3. Let f(x) be a continuous function on the interval [a,b]. If

G(t) = (the integral from a to t) f(x) dx

for a<t<b*, show that G '(t) = f(t).

*these should actually be "equal to or less than" signs, but I don't know how to type mathematical signs on a forum.
• Aug 11th 2010, 10:32 PM
Vlasev
This is just the fundamental theorem of calculus and you are asked to prove it for this interval. You enter \ge for greater or equal and \leq for less than or equal.

To do the question you should consider the difference quotient

$\displaystyle \displaystyle \frac{G(t+h)-G(t)}{h}$ then let h go to zero.
• Aug 12th 2010, 03:54 AM
HallsofIvy
To use "LaTex" on this site, enclose the code in [ math ] and [ \math ] (without the spaces). To see the code for specific math in posts, double click on it.
There is a tutorial at http://www.mathhelpforum.com/math-help/f47/
• Aug 14th 2010, 06:41 AM
blackdragon190
Still kind of unsure, but thanks for the help.