Anti derivative

**Adriana1226** · December 16th 2012, 08:07 PM

-4 square root x/2

**earboth** · December 16th 2012, 10:48 PM

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?

**Adriana1226** · December 17th 2012, 02:04 AM

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

**MarkFL** · December 17th 2012, 03:09 AM

Hint: $\sqrt{\frac{x}{2}}=\frac{\sqrt{x}}{\sqrt{2}}$ .

**x3bnm** · December 17th 2012, 03:05 PM

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

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