HH_Sec_5_3 - (9/30/08) Math 10B. Lecture Examples. Section...

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Unformatted text preview: (9/30/08) Math 10B. Lecture Examples. Section 5.3. The Fundamental Theorem and interpretations Example 1 What is the value of integraldisplay 2 F prime ( x ) dx if F ( x ) = x 4 + 5 ? Answer: integraldisplay 2 F prime ( x ) dx = 16 Example 2 Figure 1 shows the graph of the continuous derivative r = G prime ( x ) of a continuous function y = G ( x ) . Region A in the drawing has area 89 and region B has area 62. What is G ( 6 )- G ( 1 ) ? x 1 r- 20 20 40 r = G prime ( x ) A B 6 FIGURE 1 Answer: G (6)- G (1) = 27 Example 3 A tank contains 100 gallons of water at t = (minutes) and water is added at the rate of 20t gallons per minute at time t for t 4 . How much water is in the tank at t = 4 ? Answer: Figure A3 The tank has 260 gallons of water in it at t = 4 t (minutes) 4 2 r (gallons per minute) 40 80 r = 20 t Figure A3 Lecture notes to accompany Section 5.3 of Calculus by Hughes-Hallett et al....
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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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HH_Sec_5_3 - (9/30/08) Math 10B. Lecture Examples. Section...

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