## Finding the definite integral of a constant?

on 16 Jan 2013

### Shashank Prasanna (view profile)

Hello. I'm writing a program for class which solves Gauss's Law numerically and plots points. The problem I'm running into is in the integral. Gauss's Law for a sphere can be rearranged into two definite integrals: the integral of sin(theta) from 0 to pi and the integral of 1 from 0 to 2pi. I used trapz for both:

```theta = 0:pi/100:pi;
polarintegral = sin(theta);
phi = 0:pi/100:2*pi;
azimuthintegral = 1;
polar = trapz(theta, polarintegral);
azimuth = trapz(phi, azimuthintegral);
```

The theta integral works perfectly. Matlab, however, doesn't seem to understand how to integrate 1, since it's not a function of phi. The project instructions says that we're not allowed to solve the integral for the program, even if it's simple. Does anybody have any ideas how I might be able to fix this snag?

By the way, I'm using Matlab 2009b in case that makes a difference. Thank you!

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### Shashank Prasanna (view profile)

on 16 Jan 2013
Edited by Shashank Prasanna

### Shashank Prasanna (view profile)

on 16 Jan 2013

Maybe you want to do this instead:

az = ones(length(phi),1);

azimuth = trapz(phi, az)

Rachel

### Rachel (view profile)

on 16 Jan 2013

Thank you so much! It worked perfectly and now my program runs like it should! Now to adapt it for the more complex problems.

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