Integrating Square Roots

• Sep 15th 2009, 08:53 PM
actuary.101
Integrating Square Roots
Hello, I was just wondering if you all could help me integrate functions like square root(2x^2) or square root(x^4)

Also, I am not sure how to get square root symbols, super/subscripts, etc. on this forum. Could anyone help me with that?

• Sep 15th 2009, 08:56 PM
seld
so you can treat a square root like a power because you know that:

you do "[tex]" and put your math stuff and then put "[/ math]"

for the square root (x) you type "\sqrt{x}"

$\displaystyle \sqrt{x}=x^{\frac{1}{2}}$

and you can just evaluate using power rule.

$\displaystyle \frac{d}{dx}(x^{\frac{1}{2}})=\frac{1}{2}*x^{-\frac{1}{2}}$

So what I typed between the math things was:
\sqrt{x}=x^{\frac{1}{2}}

\frac{x}{y} gives you a fraction of x/y.

For subscripts you just type say you want:

$\displaystyle x_0$

you type x_0 the "_" signifies a subscript and the "^" signifies a superscript

I learned it by just reading what people typed and googling, you can basically click on the latex script that people use and it'll pop up something that you can look at, so you can copy and try things out for yourself.

I also test things at:

LaTeX Equation Editor - SITMO
• Sep 15th 2009, 09:09 PM
actuary.101
I really appreciate the help for everything :)

As far as these problems go, I am talking about taking the anti-derivative of these functions.
• Sep 15th 2009, 10:34 PM
seld
hahaha wow talk about being blind, I guess that's what happens when you're food deprived.

Hmm . . . well okay so you know power rule right?

$\displaystyle \frac{d}{dx}(x^n)=nx^{n-1}$

Well for an integral you just reverse it.

so power rule for an integral is:

$\displaystyle \int x^ndx=\frac{x^{n+1}}{n+1}+C$

You can verify this:

so say y=x^2

$\displaystyle \frac{dy}{dx}=2x$

So when you take the integral of 2x:

you raise the power by 1, and then divide by the raised power, so it is:

$\displaystyle 2*\frac{1}{1+1}*x^{(1+1)}$

$\displaystyle 2*\frac{1}{2}*x^2$

$\displaystyle x^2$
• Sep 16th 2009, 04:54 AM
HallsofIvy
Quote:

Originally Posted by actuary.101
Hello, I was just wondering if you all could help me integrate functions like square root(2x^2) or square root(x^4)

Also, I am not sure how to get square root symbols, super/subscripts, etc. on this forum. Could anyone help me with that?

For these particular functions, it helps to know that $\displaystyle \sqrt{2x^2}= \sqrt{2} |x|$ and $\displaystyle \sqrt{x^4}= x^2$. Those are surely easier to integrate.