HH_Sec_5_4 - (9/30/08) Math 10B. Lecture Examples. Section...

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Unformatted text preview: (9/30/08) Math 10B. Lecture Examples. Section 5.4. Theorems about definite integrals† Example 1 What is the integral of g from 1 to 8 if its integral from 1 to 5 is −7 and its integral from 5 to 8 is 9? 8 Answer: 1 g (x) dx = 2 35 35 35 Example 2 What is −35 35 [2p(x) − 3q(x)] dx if −35 p(x) dx = 10 and −35 q(x) dx = 20? Answer: −35 [2p(x) − 3q (x)] dx = −40 0 4 3 Example 3 What is 3 0 Y(x) dx if 0 Y(x) dx = 100 and 4 Y(x) dx = −25? Answer: 3 Y (x) dx = −75 3 3 3 Example 4 What is 0 3 [2f (x) − 4g(x)] dx if 0 f (x) dx = 100 and 0 g(x) dx = 200? Answer: 0 [2f (x) − 4g (x))] dx − 600 Example 5 Use the formulas for areas of rectangles and circles to evaluate 2 (5 − 3 0 2 4 − x2 ) dx. 4 − x2 ) dx = 10 − 3π Answer: 0 (5 − 3 Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡ Section 6.2: Example 6 notes to accompany Section 5.4 of Calculus by Hughes-Hallett et al. 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 † Lecture 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.

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