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# Finding the definite integral of a constant?

Asked by Rachel on 16 Jan 2013

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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Answer by Shashank on 16 Jan 2013
Edited by Shashank on 16 Jan 2013

Maybe you want to do this instead:

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

azimuth = trapz(phi, az)

## 1 Comment

Rachel 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.