1
$\begingroup$

In the below integral, given that $a$, $\sigma$, $\epsilon$ are constants, how do I pull them outside the integration sign? $E =\int_{0}^{\pi}{\frac{a^2\sigma \sin\theta}{2\epsilon\sqrt{a^2-x^2-2ax\cos\theta}}d\theta}$

In fact i need to show that $E = \frac{a^2\sigma}{\epsilon x}$

  • 2
    The formula for E is false. Try x=0.2012-09-10

1 Answers 1

1

I suppose you have an error on $-x^2$.

If you set $t=\sqrt{a^2+x^2-2ax\cos\theta}$, you have

$dt=\frac{ax\sin\theta}{\sqrt{a^2+x^2-2ax\cos\theta}}d\theta$

so that the integral becomes (supposing $x+a>0$ and $x-a>0$)

$ E=\int_{x-a}^{x+a}\frac{a\sigma}{2\epsilon x}dt=\frac{a^2\sigma}{\epsilon x} $