1. Average Values & Other Antiderivative Applications
Lesson 7.1

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

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 – t2)
What is the average amount of the water in the tank while it is draining?

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

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

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. Current and Power
An 80-μF capacitor is charged to 100 V. It is then supplied a current of i=0.04t3 A.
After what time interval does the capacitor voltage reach 225 V?

9. Any one of these can be substituted in to the formula above
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. Work The power of a certain electrical system is charged according to
What is the formula for energy in this circuit?

11. Assignment
Lesson 7.1
Page 262
Exercises 1 – 21 odd