1. Unit 6 – Fundamentals of Calculus Section 6
Unit 6 – Fundamentals of Calculus Section 6.7 – The Definite Integral No Calculator

2. Fundamental Theorem of Calculus
If f is continuous on [a, b] and F is any antiderivative on [a, b],
then 36 20

3. 15 10 6

4. Find the area under the curve
from x = 0 to x = 1

5. Find the area under the curve
from x = 1 to x = 2

6. Average Value of a Function on [a, b]
Find the average value of on the interval [-2, 2]

7. Average Value of a Function on [a, b]
Find the average value of on [-1, 1]

8. DIFFERENTIATE
POSITION s(t)
VELOCITY v(t)
ACCELERATION a(t)
INTEGRATE

9. Given on [0, 10], find the net distance traveled.

10. Given on [1, 2], find the net distance traveled.

11. Averages Average Value of a Function Average value of f(x)
Average Rate of Change
Average value of f ’(x)

12. Given on [2, 4]:
a) Find
b) Find the average position on the interval [2, 4]
c) Find the average velocity on the interval [2, 4]

13. Given on [1, 3]:
a) Find s(2) if s(0) = 3
b) Find the average acceleration
c) Find the acceleration at t = 3

14. Given on [0, 4] with v(1) = 5 and s(0) = 2:
a) Find s(1)
b) Find the average acceleration.