# Integral of this exponential

1. Oct 22, 2014

Hey guys,

if I have an integral of the form $\int d^{3}x \hspace{2mm} e^{i(k\cdot x)}$, how do I evaluate this?

Thanks a bunch...

2. Oct 22, 2014

### Staff: Mentor

Is that d a constant, or the differential operator, or what?

3. Oct 22, 2014

its the integration of measure, over 3 spatial dimensions

4. Oct 23, 2014

### Vagn

How can you rewrite the exponential? Maybe try using Euler's formula if you aren't confident with the exponential.

5. Oct 23, 2014

### clem

Write ${\bf k\cdot x}=kx\cos\theta$. Then do the angular integration.

6. Oct 23, 2014

### Staff: Mentor

Or in Cartesian coordinates, write out the dot product in terms of components: $\vec k \cdot \vec x = k_x x + k_y y + k_z z$.

7. Oct 23, 2014

### Meir Achuz

$\int d^{3}x \hspace{2mm} e^{i(k\cdot x)}=(2\pi)^3\delta({\bf r})$, the Dirac delta function.

8. Oct 23, 2014