Taylor series for with an integral












1












$begingroup$


I was trying to analyze a large amplitude problem and I got stuck at an equation like this.



$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.



I went online to find a solution but found none so far.



I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.



It seems (?) that I have to find an approximation to an elliptic integral.






integration taylor-expansion







share|cite|improve this question











$endgroup$












  • $begingroup$
    Have to find an approximation to elliptic integral
    $endgroup$
    – Swap Nayak
    Jan 30 at 16:12
















1












$begingroup$


I was trying to analyze a large amplitude problem and I got stuck at an equation like this.



$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.



I went online to find a solution but found none so far.



I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.



It seems (?) that I have to find an approximation to an elliptic integral.






integration taylor-expansion







share|cite|improve this question











$endgroup$












  • $begingroup$
    Have to find an approximation to elliptic integral
    $endgroup$
    – Swap Nayak
    Jan 30 at 16:12














1












1








1





$begingroup$


I was trying to analyze a large amplitude problem and I got stuck at an equation like this.



$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.



I went online to find a solution but found none so far.



I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.



It seems (?) that I have to find an approximation to an elliptic integral.






integration taylor-expansion







share|cite|improve this question











$endgroup$




I was trying to analyze a large amplitude problem and I got stuck at an equation like this.



$$int_0^T dt=sqrt{frac{l}{2g}}int_{theta_{text{max}}}^{ theta_0} frac{d theta }{ sqrt{costheta - cos theta_{text{max}}}}$$
where everything is constant except the dummy integration variable $t$ and $theta$.



I went online to find a solution but found none so far.



I thought about an infinite Taylor series: Let $y$ be the required function on the right hand side, then $frac{dy}{dtheta}$ will be the known function itself.
$$ y = y(0)+y'(0) + y''(0)ldots$$
I was able to calculate $y(0)$ as an indefinite integral. But there are limits in my integral. I am not sure if this is how I approach the problem.



It seems (?) that I have to find an approximation to an elliptic integral.






integration taylor-expansion




integration taylor-expansion






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Feb 1 at 2:17









Lee David Chung Lin

4,47841242




4,47841242










asked Jan 30 at 9:58









Swap NayakSwap Nayak

72




72












  • $begingroup$
    Have to find an approximation to elliptic integral
    $endgroup$
    – Swap Nayak
    Jan 30 at 16:12


















  • $begingroup$
    Have to find an approximation to elliptic integral
    $endgroup$
    – Swap Nayak
    Jan 30 at 16:12
















$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12




$begingroup$
Have to find an approximation to elliptic integral
$endgroup$
– Swap Nayak
Jan 30 at 16:12










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