AP Calculus AB – Chapter 4 Test – Part II
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CALCULATORS OK!!
x
2
5
7
8
f(x)
10
30
40
20
1. The function f is continuous on the interval [2,8] and has values as shown in the table
above. Use the subintervals [2,5], [5,7], and [7,8] to find the trapezoidal approximation
8
of ∫2 𝑓(𝑥)𝑑𝑥
(A)
110
(B) 130
(C) 160
(D)
190
(E) 210
2. At time t≥ 0, the acceleration of a particle moving on the x-axis is a(t) = t + sin(t). At t =
0, the velocity of the particle is -2. For what value of t will the velocity of the particle be
zero?
(A) 1.025
(B) 1.478
(C) 1.85 4
(D) 2.810
(E) 3.142
3. The average value of 𝑦 = 𝑥 2 √𝑥 3 + 1 on the interval [0,2] is
(A) 26/9
(B) 52/9
(C) 26/3
(D) 52/3
(E) 24
4. Express the following integral as an equivalent integral WITHOUT the absolute value.
Then evaluate the integral using the calculator.
3
∫0 |𝑥 2 + 2𝑥 − 3|𝑑𝑥 =
(A) 9
(B) 37/6
(C) 37/3
(D) -37/3
(E) -9
5. Using u-substitution, the indefinite integral ∫(𝑥 2 + 1)(𝑥 3 + 3𝑥−7)3/5 𝑑𝑥 =
(A)
(D)
5
24
5
16
5
1
(𝑥 3 + 3𝑥 − 7)8/5 + 𝐶 (B) 8 (𝑥 3 + 3𝑥 − 7)8/5 + 𝐶 (C) 3 (𝑥 3 + 3𝑥 − 7)2/5 + 𝐶
(𝑥 2 + 1)2 (𝑥 3 + 3𝑥 − 7)8/5 + 𝐶
(E)
8
15
(𝑥 3 + 3𝑥 − 7)8/5 + 𝐶
6. Given the velocity of an object in ft/sec., find the displacement and total distance
traveled in the given time interval. v(t) = t2 - 10t + 16, [0,6]
7. Find an equation for f(x) whose derivative f’(x) = 4 sin (20x) and whose graph passes
𝜋
through the point (20 ,
8.
−4
5
).
A squirrel starts at building A at
time t = 0 and travels along a
straight wire connected to
building B.
For 0 ≤ t ≤ 18, the squirrel’s
velocity is modeled by the
piecewise-linear function defined
by the graph at the left.
.
(a) At what times in the interval 0 < t < 18, if any, does the squirrel change direction? Give a
reason for your answer.
(b) At what time in the interval 0 ≤ t ≤ 18 is the squirrel farthest from building A ? How far
from building A is the squirrel at this time?
(c) Find the total distance the squirrel travels during the time interval 0 ≤ t ≤ 18.
(d) Write expressions for the squirrel’s acceleration a(t ), velocity v(t ), and distance x(t )
from building A that are valid for the time interval 7 < t < 10.
.