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Unformatted text preview: (9/30/08) Math 10B. Lecture Examples. Section 7.5. Approximating deﬁnite integrals†
1 Example 1 Calculate the Midpoint Rule approximation of
0 x2 dx corresponding to the partition of [0,1] into ﬁve equal subintervals. Draw the curve y = x2 with the rectangles whose areas give the approximation. Answer: Figure A1. • [Midpoint Rule approximation] = 0.33 y 1 y = x2 Figure A1 1 x 15 Example 2 Calculate the Trapezoid Rule approximation of
0 g(x) dx with three subintervals for the function y = g(x) of Figure 1. Draw the trapezoids whose areas give the approximation. y 150 100 50 FIGURE 1 y = g ( x) 5 10 15 x Answer: Figure A2 • [Trapezoid-Rule approximation] = 1275 † Lecture notes to accompany Section 7.5 of Calculus by Hughes-Hallett et al. 1 Math 10B. Lecture Examples. (9/30/08) y 150 100 50 Figure A2 Section 7.5, p. 2 y = g ( x) 5
30 10 15 x Example 4 Give the Trapezoid Rule approximation of
0 x2 dx with three subintervals.
Answer: [Trapezoid Rule approximation] = 9500 Example 5 The next table gives the rate r = r(t) (million metric tons per year) at which grain was produced in the world at ten-year intervals from 1950 to 1990.(1) Use the Trapezoid Rule to estimate the total world grain production from the beginning of 1950 to the beginning of 1990. Year r (t ) 1950 631 1960 847 1970 1096 1980 1447 1990 1780 Answer: [Total production] ≈ 45,955 million metric tons of grain Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡ Section 6.6: Examples 4a and 4b Data adapted from Vital Signs, 1992, p. 25. Source: USDA, World Grain Database. chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course.
‡ The (1) ...
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.
- Summer '10