Question

refer to the figure to the right. set up a definite integral that represents the shaded area from a to b.

Explanation:

Step1: Recall the formula for the area under a curve

The area \(A\) under the curve \(y = f(x)\) from \(x=a\) to \(x = b\) is given by the definite integral \(A=\int_{a}^{b}f(x)dx\) when \(f(x)\geq0\) on the interval \([a,b]\). In the given figure, the function \(y = f(x)\) is above the \(x -\)axis (since the area is shaded and we assume the standard interpretation of area in the Cartesian plane for such problems), so we can directly apply the formula.

Answer:

\(\int_{a}^{b}f(x)dx\)