## 2.4Calculating the Area Below or Above a Curve

Sometimes it is useful to be able to measure the size of the area below or above a curve. For the sake of simplicity, we’ll only calculate the area below or above a linear curve.

How large is the shaded area below the linear curve in panel (a) of Figure 2A-7? First note that this area has the shape of a right triangle. A right triangle is a triangle that has two sides that make a right angle with each other. We will refer to one of these sides as the height of the triangle and the other side as the base of the triangle. For our purposes, it doesn’t matter which of these two sides we refer to as the base and which as the height.

Figure 2.7: FIGURE 2A-7 Calculating the Area Below and Above a Linear Curve
Figure 2.7: The area above or below a linear curve forms a right triangle. The area of a right triangle is calculated by multiplying the height of the triangle by the base of the triangle, and dividing the result by 2. In panel (a) the area of the shaded triangle is . In panel (b) the area of the shaded triangle is .

Calculating the area of a right triangle is straightforward: multiply the height of the triangle by the base of the triangle, and divide the result by 2. The height of the triangle in panel (a) of Figure 2A-7 is 10 − 4 = 6. And the base of the triangle is 3 − 0 = 3. So the area of that triangle is

How about the shaded area above the linear curve in panel (b) of Figure 2A-7? We can use the same formula to calculate the area of this right triangle. The height of the triangle is 8 − 2 = 6. And the base of the triangle is 4 − 0 = 4. So the area of that triangle is