Quote:
Originally Posted by galactus  For goodness sake, why didn't you say that in the first place?. That makes all the difference. It's the second fundamental rule of calc. There is no need to laboriously find the integral.
Is this what it is: ![\frac{d}{dx}\left[\int_{a}^{x}f(t)dt\right]=f(x)](http://www.mathhelpforum.com/math-help/latex2/img/62ad2b1f48620a678a35fe712d23347b-1.gif "\frac{d}{dx}\left[\int_{a}^{x}f(t)dt\right]=f(x)")
For instance, ![\frac{d}{dx}\left[\int_{1}^{x}\frac{sin(t)}{t}dt\right]=\frac{sin({\color{red}x})}{{\color{red}x}}](http://www.mathhelpforum.com/math-help/latex2/img/8afe9b51cb70437ca6b4121a97fa18ef-1.gif "\frac{d}{dx}\left[\int_{1}^{x}\frac{sin(t)}{t}dt\right]=\frac{sin({\color{red}x})}{{\color{red}x}}")
Remember that  |
Just being picky
To the OP : why isn't there sin(1) ?
Imagine that
is an antiderivative of your function f.
We know that
But a is a constant with respect to x. So F(a) is a constant too.
Hence when differentiating, you'll only have
, which is exactly
