# Showing an integral doesn't converge

1. May 17, 2010

### scigal89

1. The problem statement, all variables and given/known data

Show that the following function is not square integrable, i.e. that it is not continuous.

$$\int_{-\infty}^{\infty} \left ( e^{ikx} \right )^{2}dx$$

2. Relevant equations

See above. Also:

$$\int \left ( e^{ikx} \right )^{2}dx = -\frac{ie^{2ikx}}{2k}$$

3. The attempt at a solution

$$=\lim_{A \rightarrow -\infty}\int_{A}^{C} e^{2ikx}dx+\lim_{B \rightarrow \infty}\int_{C}^{B} e^{2ikx}dx$$

How do I go from there? What would I choose for C? Can it be anything?

Last edited: May 17, 2010
2. May 17, 2010

### LCKurtz

Not being square integrable is not the same as not being continuous. f(x) = 1 is not square integrable on (-oo, oo) but is obviously continuous.

Yes, you can use anything for C. And if either integral diverges the whole thing does.