1. Average Values & Other Antiderivative Applications Lesson 7.1

2. 2 Average Value of a Function Consider recording a temperature each hour and taking an average If we take it more often and take a limit …

3. 3 Average Value of a Function Now apply the concept to a continuous function f(x) a b

4. 4 Application A 20,000 L water tank takes 10 min. to drain. After t min the water left in the tank is V(t) = 200(100 – t 2 ) What is the average amount of the water in the tank while it is draining?

5. 5 Root Mean Square Used to calculate the effective current and effective voltage of alternating current Root mean square

6. 6 Root Mean Square If current is given by What is the effective current for the time interval from 0 < t < 4

7. 7 Current and Power Current, i defined as the time rate of change of the charge, q  Given in coulombs  Passing through a given point in the circuit Total charge transmitted in a circuit Voltage between terminals of capacitor with C farads

8. 8 Current and Power An 80-μF capacitor is charged to 100 V. It is then supplied a current of i=0.04t 3 A. After what time interval does the capacitor voltage reach 225 V?

9. 9 Work Work expended in an electrical system given by  W in joules  P in watts Instantaneous power represented by Any one of these can be substituted in to the formula above

10. 10 Work The power of a certain electrical system is charged according to What is the formula for energy in this circuit?

11. 11 Assignment Lesson 7.1 Page 262 Exercises 1 – 31 odd