Antiderivatives and Areas - Solutions
Math 125
In this worksheet, we explore the Fundamental Theorem of Calculus and applications of the Area
Problem to problems involving distance and velocity.
FTC Practice
1
Let
f
(
x
) be given by the graph to the right and define
A
(
x
) =
integraldisplay
x
0
f
(
t
)
dt
. Compute the following.
A
(1) =
2
A
(2) =
4
A
(3) =
6
1
2
A
(4) =
9
A
′
(1) =
2
A
′
(2) =
2
A
′
(3) =
3
A
′
(4) =
2
The maximum value of
A
(
x
) on the interval [0
,
5] is
10
1
2
The maximum value of
A
′
(
x
) on the interval [0
,
5] is
3
1
2
3
2
1
3
4
5
y=f(x)
Velocity and Distance2A toy car is travelling on a straight track. Its velocityv(t), in m/sec, be given by the graph to the right. Defines(t)to be the position of the car in meters. Choose coordinatesso thats(0) = 0. Compute the following.123

Net and Total Change
3