5-7: The 1 st Fundamental Theorem & Definite Integrals Objectives: Understand and apply the 1 st Fundamental Theorem ©2003 Roy L. Gover

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Presentation transcript:

5-7: The 1 st Fundamental Theorem & Definite Integrals Objectives: Understand and apply the 1 st Fundamental Theorem ©2003 Roy L. Gover

Theorem If f is continuous on [ a,b ] and F is an antiderivative of f on [ a,b ], then: The 1 st Fundamental Theorem of Calculus:

Example Evaluate the definite integral using a Riemann Sum the 1 st fundamental theorem:

Try This Evaluate the definite integral using the 1 st fundamental theorem:

Try This Evaluate the definite integral using the 1 st fundamental theorem: 4

Try This Evaluate the definite integral using the 1 st fundamental theorem: 1

Try This Find the area bounded by, the x axis, the y axis and the line x = sq. units

Important Idea Provided you can find an antiderivative of f, you can now evaluate a definite integral without using the limit of a Riemann sum.

Try This Evaluate: =0

Theorem If f is integrable on a closed interval containing the three points a, b, and c, then:

Example Evaluate the definite integral

Example Find the area bounded by,the x axis, and the lines x =-2 and x =2 -2 2