When students work on area problems with integration, they often make some common mistakes. Here are a few important ones to keep an eye on:

1. Not Setting Up the Integral Correctly: It’s really important to make sure the limits of the integral match the area you want to find. If you are trying to find the space between two curves, make sure you know where the curves cross each other and use those points as your limits.

2. Forgetting to Substitute Properly: If you're using substitution, don’t forget to change the limits of integration. For example, if you have $u = g(x)$, when your $x$ changes from $a$ to $b$, then $u$ will change from $g(a)$ to $g(b)$.

3. Missing Constant Factors: When you use integration by parts, remember this rule:

   $\int u \, dv = uv - \int v \, du$

   Sometimes, students forget to take care of the $dv$ part right.

By avoiding these mistakes, students can get better at solving area problems and feel more confident!