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5-7: The 1 st Fundamental Theorem & Definite Integrals Objectives: Understand and apply the 1 st Fundamental Theorem ©2003 Roy L. Gover (roygover@att.net)
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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:
![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:](http://images.slideplayer.com./39/10843048/slides/slide_3.jpg "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:")
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Example Evaluate the definite integral using a Riemann Sum the 1 st fundamental theorem:
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Try This Evaluate the definite integral using the 1 st fundamental theorem:
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Try This Evaluate the definite integral using the 1 st fundamental theorem: 4
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Try This Evaluate the definite integral using the 1 st fundamental theorem: 1
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Try This Find the area bounded by, the x axis, the y axis and the line x =2. 0 2 sq. units
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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.
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Try This Evaluate: =0
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Theorem If f is integrable on a closed interval containing the three points a, b, and c, then:
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Example Evaluate the definite integral
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Example Find the area bounded by,the x axis, and the lines x =-2 and x =2 -2 2
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