# Thread: convergence test for integral

1. ## convergence test for integral

hey there.. i'm kinda lost here..
i need to do convergence test for the equation below...
$\displaystyle y(x)=\frac{1}{\sqrt{2\pi}}\frac{1}{a}\sqrt{\frac{\ pi}{a}}\int_{-\infty}^{\infty} e^{-a|x|}f(x-t)dt$

however.. i've got 2 value of f(x).. e^x^2 and x^5

how am i going to test them?
should i include my f(x) inside the equation above?
like this...
$\displaystyle y(x)=\int_{-\infty}^{\infty} e^{-a|x|}f(x-t)^{5}dt$

and..

$\displaystyle y(x)=\int_{-\infty}^{\infty} e^{-a|x|}f(e^{(x-t)^{2}})dt$

2. If f(x) = $\displaystyle x^5$, then the substitution gives

$\displaystyle y(x)=(constants)\int_{-\infty}^{\infty} e^{-a|x|}(x-t)^{5}dt$

Similarly,

If f(x) = $\displaystyle e^{x^2}$, then the substitution gives

$\displaystyle y(x)=(constants)\int_{-\infty}^{\infty} e^{-a|x|}e^{(x-t)^{2}}dt$

3. how am i going to test the equations?