Integration issue

3 posts / 0 new
Last post
Integration issue

After deriving an equation I have ended up with equation where I have a complex denominator and I am not sure how to simplify. I am trying to work out as a function of x. Equation link is below. Thanks in advance.

Jhun Vert
Jhun Vert's picture

\dfrac{p}{\dfrac{Ao\left( \dfrac{1 - x}{2L} \right)}{E}} & = \dfrac{2pEL}{Ao(1 - x)} \\
& = \dfrac{2pEL}{Ao} \cdot \dfrac{1}{1 - x}

You posted this with a title "integration issue" under calculus, which I presume you wanted to do this:
$\displaystyle \dfrac{2pEL}{Ao} \int \dfrac{dx}{1 - x} = -\dfrac{2pEL}{Ao}\ln (1 - x) + C$

Side Note:

Allow me to bring up your previous post which is a little similar to the equation in this post.


The only difference is E.

Note that
$\dfrac{p}{\dfrac{Ao\left( \dfrac{1 - x}{2L} \right)}{E}} = \dfrac{p}{Ao\left( \dfrac{1 - x}{2L} \right)} * E$

$\dfrac{p}{Ao\left( \dfrac{1 - x}{2L} \right)} * E^{-1} = \dfrac{p}{AoE\left( \dfrac{1 - x}{2L} \right)}$

I am not sure though if this side note is still relevant to you.


Romel, this is excellent.

If you get chance, could you explain some of the steps i.e. not sure how E is positive and a numerator, and in addition the ln(1-x). Thanks in advance Paul

Add new comment

Deafult Input

  • Allowed HTML tags: <img> <em> <strong> <cite> <code> <ul> <ol> <li> <dl> <dt> <dd> <sub> <sup> <blockquote> <ins> <del> <div>
  • Web page addresses and e-mail addresses turn into links automatically.
  • Lines and paragraphs break automatically.
  • Mathematics inside the configured delimiters is rendered by MathJax. The default math delimiters are $$...$$ and \[...\] for displayed mathematics, and $...$ and \(...\) for in-line mathematics.

Plain text

  • No HTML tags allowed.
  • Lines and paragraphs break automatically.