Introduction to Integrals
Problems for "Average Value and Second Fundamental Theorem"
f (x)dx
x
3-3x
2
-1
1
1-3
-(-1-3)
-cos(x)
-Π
Π
-
-1
-(-(-1))
Problem :
For the function above, find the
c
on
[- Π, Π]
such that
f (c) = f
avg
Problem : Use the second fundamental theorem of calculus to find F' .
F(x) =  (9t+9)dt
|
Problem : Now integrate the above expression for F and then take the derivative to find F'(x) and verify the result from the previous question.
|
F(x) = (9t+9)dt
|
9t+9
dt = 
t
2+9t
2
x
- (18 + 18)
