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HH_Sec_5_3

# HH_Sec_5_3 - Math 10B Lecture Examples Section 5.3 The...

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(9/30/08) Math 10B. Lecture Examples. Section 5.3. The Fundamental Theorem and interpretations Example 1 What is the value of integraldisplay 2 0 F prime ( x ) dx if F ( x ) = x 4 + 5 ? Answer: integraldisplay 2 0 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 = 0 (minutes) and water is added at the rate of 20t gallons per minute at time t for 0 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. 1

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Math 10B. Lecture Examples. (9/30/08) Section 5.3, p. 2 Example 4 An object moving on an s -axis with coordinates given in feet is at s = 10 at time t = 1 . The graph of its velocity v ( t ) = s prime ( t )
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HH_Sec_5_3 - Math 10B Lecture Examples Section 5.3 The...

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