- #1
TehAdzMan
- 6
- 0
Hi,
So this is part of an assignment for my numerical analysis class.
The integral is this:
[tex]
\int_0^{\infty} e^{-x} \cos^2 (x^2) dx
[/tex]
We are instructed to evaluate the integral from 0 to some large A using numerical methods (which I'm fine with), and then estimate the tail, ie the integral from A to infinity.
Basically we need to come up with some method to estimate and bound the remainder in the tail.
My idea was to substitute [tex] u = x^2 [/tex] which gives [tex] \int_A^{\infty} \frac{e^{- \sqrt{u}} \cos^2(u)}{\sqrt{u}} du [/tex]
and then I guess take the maximum of the cos function as 1 and just remove it, and use the remaining function, which I think would be quite easy to integrate and would give a maximum bound.
Any thoughts greatly appreciated.
Regards,
Adam
So this is part of an assignment for my numerical analysis class.
The integral is this:
[tex]
\int_0^{\infty} e^{-x} \cos^2 (x^2) dx
[/tex]
We are instructed to evaluate the integral from 0 to some large A using numerical methods (which I'm fine with), and then estimate the tail, ie the integral from A to infinity.
Basically we need to come up with some method to estimate and bound the remainder in the tail.
My idea was to substitute [tex] u = x^2 [/tex] which gives [tex] \int_A^{\infty} \frac{e^{- \sqrt{u}} \cos^2(u)}{\sqrt{u}} du [/tex]
and then I guess take the maximum of the cos function as 1 and just remove it, and use the remaining function, which I think would be quite easy to integrate and would give a maximum bound.
Any thoughts greatly appreciated.
Regards,
Adam