4 Integrals.

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Presentation transcript:

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.