5.3 - The Definite Integral - Haas

# 5.3 - The Definite Integral - Haas - region bounded by the...

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Calculus I - Section 5.3 Change the directions for problems 27-42 to: Evaluate the integrals using the definition of the definite integral. Definition of the Definite Integral If f is defined on the closed interval and the limit exists, then f is integrable on and the limit is called the definite integral of f from a to b . We say, . If the partition of the interval has n equal subintervals, then we have . Example: Use the definition of the definite integral to evaluate 3 2 dx x

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The Definite Integral as the Area of a Region If f is continuous and nonnegative on the closed interval [a,b], then the area of the
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Unformatted text preview: region bounded by the graph of , the x-axis, and the vertical lines x=a and x=b is given by Area = Note that in the previous example our function was not nonnegative over the interval. Therefore, the integral did not represent an area. b a dx x f ) ( Properties of Definite Integrals If is defined at x=a, then If is integrable on [a,b], then If is integrable on the three closed intervals determined by a,b, and c, then ) ( a a dx x f b a a b dx x f dx x f ) ( ) ( b c c a b a dx x f dx x f dx x f ) ( ) ( ) (...
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## This note was uploaded on 01/12/2012 for the course MATH 2554 taught by Professor Pamelasatterfield during the Spring '11 term at NorthWest Arkansas Community College.

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5.3 - The Definite Integral - Haas - region bounded by the...

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