4 Integrals
4.2 The Definite Integral
Riemann Sum
The Definite Integral The symbol was introduced by Leibniz and is called an integral sign. f (x) is called the integrand and a and b are called the limits of integration can be interpreted as the area under the curve y = f (x) from a to b.
The Definite Integral A definite integral can be interpreted as a net area, that is, a difference of areas: where A1 is the area of the region above the x-axis below the graph of f, and A2 is the area of the region below the x-axis above the graph of f. is the net area.
Net Area on interval [-1,9]? Total Area on interval [-1,9]?
Example 1:
Example 2:
Example 3: Area
Properties of the Definite Integral
Practice 1 Use the properties of integrals to evaluate Solution:
Practice 1 – Solution cont’d So
Practice 2 Solution in class.
Practice 3 a) b) Solutions in class.