Absolute values and piecewise functions

Material by the IntegralPaso project. Conditions and limits are stated in each guide; external teaching review is pending.

Locate formula or sign changes and split the interval. Integrate each expression on its own piece and add the results. For continuous global primitives adjust constants between pieces when possible.

Step-by-step example

1. Split where the sign changes.

   $$\int_{-1}^2|x|\,dx=\int_{-1}^0(-x)\,dx+\int_0^2x\,dx$$

2. Evaluate each piece separately.

   $$I=1/2+2$$

3. Add the positive areas.

   $$I=5/2$$