Math 22 Area and the Fundamental Theorem of Calculus
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Definition of a Definite Integral
Let be nonnegative and continuous on the closed interval . The area of the region bounded by the graph of , the x-axis, and the lines and is denoted by The expression is called the definite integral from a to b, where a is the lower limit of integration and b is the upper limit of integration.
The Fundamental Theorem of Calculus
If is nonnegative and continuous on the closed interval [a,b], then where is any function such that for all in [a,b]
Properties of Definite Integrals
Let and g be continuous on the closed interval [a,b].
1. for is constant. 2. 3. for 4. 5.
1) Find the area of the region bounded by the x-axis and the graph of when