lect116_23rev_f11

lect116_23rev_f11 - Friday, November 4 Lecture 23 : The...

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Friday, November 4 Lecture 23 : The definite integral (Refers to Section 5.2 in your text) Students who have mastered the content of this lecture know about : The definition of the definite integrals, area, net area Students who have practiced the techniques presented in this lecture will be able to : Compute the definite integral by using its definition. 23.1 Definition – Suppose we are given a continuous function f ( x ) over an interval [ a , b ] subdivided into n equal subintervals x 0 = a , x 1 , x 2 , …, x n 1 , x n = b each of length x = x i x i 1 . For each subinterval [ x i 1 , x i ] let x i * denote the right-endpoint . Then is abbreviated by the expression This expression is called the definite integral of f over [ a , b ]. When viewed in this context the numbers a and b are referred to as the limits of integration , f ( x ) is referred to as the integrand and “ dx ” as the differential . Note that, at this point, the symbol “ dx plays no role in the computation of the value of the definite integral. Many prefer to view it as a symbol which states explicitly what the variable is in the integrand.
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lect116_23rev_f11 - Friday, November 4 Lecture 23 : The...

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