- Theorem 3 4 Graphic Multiplication If F X And I X Are Positive Or Negative Linear Functions Defined On An Interval 1 (22.87 KiB) Viewed 20 times
- Theorem 3 4 Graphic Multiplication If F X And I X Are Positive Or Negative Linear Functions Defined On An Interval 2 (2.87 KiB) Viewed 20 times
Theorem 3.4 (Graphic Multiplication) If f(x) and I(x) are positive (or negative) linear functions defined on an interval [a, b], respectively, the following integral can be expressed as: 1 = [ f(x)/(x) dx (3.46) It can then be evaluated by: 1 = ±w|1(x₂)| (3.47) where wo and x are the area and centroid of the region under the graph of y=f(x), respectively. See Figure (3.17a). The integral I is positive when f(x) and 1(x) have the same sign. Otherwise, I is negative.
0 f(x) 00 b x