Anti derivative

• December 16th 2012, 09:07 PM
Anti derivative
-4 square root x/2
• December 16th 2012, 11:48 PM
earboth
Re: Anti derivative
Quote:

Originally Posted by Adriana1226
-4 square root x/2

Until today I was under the impression that even in North Carolina the freedom of speech was guaranteed. Obviously I am mistaken ...

After polishing my crystal sphere I assume that you want to determine

$\displaystyle{\int \left(-4 \cdot \sqrt{\frac x2} \right) dx}$

or

$\displaystyle{\int \left(-4 \cdot \frac{\sqrt{ x}}2 \right) dx}$

Which one do you want to do and where are your difficulties that you can't proceed?
• December 17th 2012, 03:04 AM
Re: Anti derivative
The first one. I know that when its square root of x it can become x^1/2 but what about when it's square root of x/2. What's the anti derivative
• December 17th 2012, 04:09 AM
MarkFL
Re: Anti derivative
Hint: $\sqrt{\frac{x}{2}}=\frac{\sqrt{x}}{\sqrt{2}}$.
• December 17th 2012, 04:05 PM
x3bnm
Re: Anti derivative
Quote:

Originally Posted by Adriana1226
-4 square root x/2

\begin{align*}\displaystyle{\int \left(-4 \cdot \sqrt{\frac x2} \right) dx} =& \frac{(-8)\cdot(x)^{\frac{3}{2}}}{3\sqrt{2}} + C \\ =& \frac{-4\sqrt{2}\cdot(x)^{\frac{3}{2}}}{3} + C\end{align*}

You can check the answer:

int -4 (x/2)^(1/2) - Wolfram|Alpha