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Calculate the arclength of $$y=\frac{\sqrt{x}(x^2+2)}{3}, \hspace{0.5cm} 2\leq x\leq 4$$

My work: I have calculated

$$1+(\frac{dy}{dx})^2=\frac{25x^4+20x^2+36x+4}{36x}$$

I need your help to solve the integral

$$\int_2^4\sqrt{\frac{25x^4+20x^2+36x+4}{36x}}dx$$

Please help me to find its EXACT VALUE.

Flip
  • 818
  • You'll probably need elliptic integrals in order to represent the value exactly. Are you familiar with techniques for evaluating elliptic integrals? – David H Jan 29 '15 at 17:30
  • @DavidH Sorry I don't know – Flip Jan 29 '15 at 17:57
  • Well, then I think you're going to have a very hard time finding the value. What's the context of the problem? Do you specifically need an exact value? – David H Jan 29 '15 at 18:10
  • @DavidH I have to find the arc length.It is an old exam problem so I cannot use any software.I have to find its exact value. – Flip Jan 29 '15 at 18:21

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