I have the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

I = \frac{a}{2} \int_{-a/2}^{a/2} x sin^{2}\left[ \pi (\frac{x}{a}-\frac{1}{2})\right], dx

[/tex]

I have set

[tex]

y= \frac{x}{a}-\frac{1}{2}

[/tex]

and

[tex]

dy = dx/a

[/tex]

When I substitute the two latter equations into the first equation I should get this:

[tex]

I = {a} \int_{-1}^{0} (2y+1) sin^{2}\left[ \pi y\right], dy

[/tex]

For some reason I get this instead:

[tex]

I = \frac{a}{2} \int_{-1}^{0} (y+\frac{1}{2}) sin^{2}\left[ \pi y\right], dy

[/tex]

I'm off by a factor of four. What am I doing wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Change of Variable issue with Integration

**Physics Forums | Science Articles, Homework Help, Discussion**