# Thread: How would one integrate this?

1. ## How would one integrate this?

I have gone through more than one calculus book and it's not exactly easy, this one. THere is nothing like this one in there. Does anyone know what one must do?

$\displaystyle \int{\sqrt{(1 + (0.6t^2 - 5.64t + 9.1)^2)}}$

David.
Oh, by the way, this is an application integral finding the length of a curve.
the $\displaystyle 0.6t^2 - 5.64t + 9.1$ is the derivative of the curve I want to finding the length of.

2. Originally Posted by Bucephalus
I have gone through more than one calculus book and it's not exactly easy, this one. THere is nothing like this one in there. Does anyone know what one must do?

$\displaystyle \int{\sqrt{(1 + (0.6t^2 - 5.64t + 9.1)^2)}}$

David.
Oh, by the way, this is an application integral finding the length of a curve.
the $\displaystyle 0.6t^2 - 5.64t + 9.1$ is the derivative of the curve I want to finding the length of.
arc length integrals are notorious for being unsolveable ... usually, one has to use technology to estimate the arclength.

wolfram alpha shows this to be an elliptic integral (extremely difficult to do by hand) ...

integral sqrt&#40;1&#43;&#40;.6x&#94;2-5.64x&#43;9.1&#41;&#94;2&#41; - Wolfram|Alpha