MATH 152 Activity 1 (Section 6.4)
Directions: Put your name and section number on the answersheet. Use scratch paper for work, meaning only put the
answers on the answer sheet. You may take this problem set home with you. Note: The second week of classes you will
pair up with someone in class to work on the activity. For this first activity, you are allowed to work together, however
each student will turn in his or her own answersheet. Calculators are NOT allowed and you may use your notes and
textbook. Failure to follow these instructions will result in a 1 point deduction. Neat handwriting is expected.
Z x
1. Let g(x) =
f (t) dt where the graph of f (t) is shown below.
0
(i) Evaluate g(18).
(ii) What is the maximum value of g(x)?
2. If g(x) =
Z
cos x
t3
x2
p
t5 + 1 dt, find g ′ (x).
Z √
x + x2 − x3
√
dx
3. Find
4
x3
Z 1
(t2 + 1)2 dt
4. Evaluate
0
4
5. Evaluate
Z
3
6. Evaluate
Z
2
−2
7. Find
Z
0
x + x2
dx
x3
|4 − x2 | dx
π/3
f (x) dx where f (x) =
sin x
if 0 ≤ x < π6
4 cos x if π6 ≤ x ≤ π3
8. Suppose an object is moving according to velocity v(t) = 2t − 7, 0 ≤ t ≤ 4. Find the displacement and distance
traveled during the first 4 seconds, where v(t) is measured in feet per second.
1