Page 127 - Calculus Demystified

CHAPTER 4
114

Fig. 4.15 The Integral
What we have learned is this: If f(x) < 0 on the interval under discussion, then
the integral of f will be a negative number. If we want to calculate positive area
then we must interject a minus sign.
Let us nail down our understanding of these ideas by considering some examples.

EXAMPLE 4.8
3 2
Calculate the (positive) area, between the graph of f(x) = x − 2x −
11x + 12 and the x-axis, between x =−3 and x = 4.

SOLUTION
Consider Fig. 4.16. It was drawn using the technique of Section 3.1, and it
plainly shows that f is positive on [−3, 1] and negative on [1, 4]. From the

Fig. 4.16