integration

• How to Set Up a Double Integral Over an Inequality-Defined Region
  To integrate over a region given by inequalities, sketch its boundary, find projection limits, and write the bounds in an order that covers it once.
• Reduction Formula for ∫ cos(nx)/cos(x) dx
  Derive the recurrence for the integral of cos(nx)/cos(x), with its base cases, a worked example, and the alternative cosine-power formula.
• What Is the Derivative of an Indicator Function, and Its Integral?
  An interval's indicator has ordinary derivative zero except at its jumps; its integral is overlap length, and its distributional derivative records those jumps.