1
$\begingroup$

I'm currently working on a math paper and I've come across this integral that I've had some difficulty tackling. I was hoping someone could give me a hint or insight.

$\int\limits x\sqrt{\sqrt{(1.04)^4+4x^2}-x^2-1}$

I've already tried substitution for $u=\sqrt{(1.04)^4+4x^2}$ and come up with a simpler integral $\frac{\pi}{4}\int u\sqrt{4u-u^2-((1.04)^4+4)}$

(Although I'm not sure if it's right)

I'd appreciate any help!

  • 0
    Wolfram Alpha does not find a closed form for this indefinite integral. If we know that $x\approx 0$, we can expand the integrand in a taylor series. In what context does this integral appear ? – 2017-01-31
  • 0
    This is not general form of integrals,use WolframAlpha. – 2017-01-31
  • 0
    I've already attempted to use WolframAlpha. The integral can be used as a solid of revolution around the y-axis to find the volume of the upper half of a Cassinian oval with parameter b/a = 1.04 (sorry, there's meant to be a 2pi before the first integral). I'm using the Shell method here btw. – 2017-01-31

0 Answers 0