Determine Signed Areas in a Problem
The solution to a definite integral gives you the signed area of a region. In some cases, signed area is what you want, but in some problems you’re looking for unsigned area.
The signed area above the x-axis is positive, but the signed area below the x-axis is negative. In contrast, unsigned area is always positive. The concept of unsigned area is similar to the concept of absolute value. So if it’s helpful, think of unsigned area as the absolute value of a definite integral.
In problems where you’re asked to find the area of a shaded region on a graph, you’re looking for unsigned area. But if you’re unsure whether a question is asking you to find signed or unsigned area, ask the professor. This goes double if an exam question is unclear. Most professors will answer clarifying questions, so don’t be shy to ask.
Suppose that you’re asked to calculate the shaded unsigned area that’s shown in this figure.