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Section 5.3: Evaluating Definite Integrals Practice HW from Stewart Textbook (not to hand in) p. 374 # 1-27 odd, 31-43 odd
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Definite Integral The definite integral is an integral of the form This integral is read as the integral from a to b of. The numbers a and b are said to be the limits of integration. For our problems, a < b. Definite Integrals are evaluated using The Fundamental Theorem of Calculus.
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Fundamental Theorem of Calculus Let be a continuous function for and be an antiderivative of. Then
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Example 1: Evaluate. Solution:
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Example 2: Evaluate. Solution:
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Additional Integration Formulas 1. 2.
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3. 4.
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Example 3: Evaluate Solution:
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Example 4: Evaluate Solution:
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Example 5: Evaluate Solution:
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Recall that if for. Then Definite Integral:
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Example 6: Find the area under the graph of on [0, 2]. Solution:
![Example 6: Find the area under the graph of on [0, 2]. Solution:](http://images.slideplayer.com/25/7667734/slides/slide_16.jpg "Example 6: Find the area under the graph of on [0, 2]. Solution:")
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Example 7: Evaluate Solution:
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Note For a function f (x) that is both positive and negative over an interval, the total area is the area enclosed by the negative part of the curve minus the negative part of the curve.
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Example 8: Consider the function over the interval. The graph of the function over this interval is given by
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Find the total area enclosed between the function and the x axis. Solution:
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