# Basic Integration Question

• Oct 18th 2010, 12:25 AM
BinaryBoy
Basic Integration Question
Hi all,

I've been learning the basics of integration recently, and as I was working through some exercises, I came across a question as seen on the attachment.

Attachment 19372

Now, I understand everything up to the part where the square root of "x" is multiplied by 2. In other words, I do not understand how (x to the power of 1/2) divided by 1/2 becomes 2 x square root(x) (a surd). I had another question where (x to the power of 3/2) divided by 3/2 simply became: 3/2 multiplied by (x to the power of 3/2). In the case of the question above, I thought the same principles applied since I am dealing with fractions.

Any help to clarify will be much appreciated!

Thanks,

Nathaniel
• Oct 18th 2010, 01:18 AM
downthesun01
$x^{\frac{1}{2}}=\sqrt{x}$

Do you agree with that?

$\frac{1}{\frac{1}{2}}=2$

Do you agree with that?

If so, then it's easy to see that $\frac {x^{\frac{1}{2}}}{\frac{1}{2}}=2\sqrt{x}$