# Thread: Evaluate integral

1. ## Evaluate integral

l don't understand the d/dx in front of the integral...

$\frac{d}{dx}\int^x_0 \frac{du}{1+u^{2}}$

= arctan 0 - arctan x

= -arctanx

could this be right?

2. Originally Posted by algebra2
l don't understand the d/dx in front of the integral...

$\frac{d}{dx}\int^x_0 \frac{du}{1+u^{2}}$

= arctan 0 - arctan x

= -arctanx

could this be right?
You need to use the fundemental theorem of calculus

$\frac{d}{dx} \int_{0}^{x}\frac{1}{1+u^2}du=\frac{1}{1+x^2}$

3. there was no reason to integrate and then differentiate, but you made mistakes in your integration....

Originally Posted by algebra2
l don't understand the d/dx in front of the integral...

$\frac{d}{dx}\int^x_0 \frac{du}{1+u^{2}}$

= ${d\over dx} (\arctan x - \arctan 0)$

= ${d\over dx} (\arctan x)$

= ${1\over 1+x^2}$

is right....
.....NOW, but is unnecessary.