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HH_Sec_7_5 - Math 10B Lecture Examples Section 7.5...

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(9/30/08) Math 10B. Lecture Examples. Section 7.5. Approximating definite integrals Example 1 Calculate the Midpoint Rule approximation of integraldisplay 1 0 x 2 dx corresponding to the partition of [0,1] into five equal subintervals. Draw the curve y = x 2 with the rectangles whose areas give the approximation. Answer: Figure A1. [Midpoint Rule approximation] = 0 . 33 x 1 y 1 y = x 2 Figure A1 Example 2 Calculate the Trapezoid Rule approximation of integraldisplay 15 0 g ( x ) dx with three subintervals for the function y = g ( x ) of Figure 1. Draw the trapezoids whose areas give the approximation. x 5 10 15 y 50 100 150 y = g ( x ) FIGURE 1 Answer: Figure A2 [Trapezoid-Rule approximation] = 1275 Lecture notes to accompany Section 7.5 of Calculus by Hughes-Hallett et al. 1
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Math 10B. Lecture Examples. (9/30/08) Section 7.5, p. 2 x 5 10 15 y 50 100 150 y = g ( x ) Figure A2 Example 4 Give the Trapezoid Rule approximation of integraldisplay 30 0 x 2 dx with three subintervals. Answer: [Trapezoid Rule approximation] = 9500
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