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MA 126 - 8C CALCULUS II
October 02, 2012
Name (Print last name first):..........................................
Student Signature:...................................................
TEST II
Closed book - No calculators!
PART I
Part I consists of 6 questions. Clearly write your answer (only) in the space provided after each question. You do not need not to show your work for this
part of the test. No partial credit is awarded for this part of the test!
Each question is worth 5 points.
Question 1
If
− 1
f (x) dx = 10 and
1
f (x) dx = −12, find the numerical value of
− 1
f (x) dx.
Answer:.....................
Question 2
Find the derivative of the function g(x) =
∫ (^) x
− 2
t^2 sin(3t) dt.
Answer:.....................
Question 3
Evaluate the definite integral ∫ (^) e 35
e^34
x
dx
(Your answer must be a real number!)
Answer:..................
Question 4
Evaluate the indefinite integral
ex ex^ + 1
dx.
Answer:..................
Question 5
Evaluate the indefinite integral
x cos(x) dx.
Answer:..................
Question 6
Evaluate the indefinite integral
x x + 5
dx.
Answer:..................
Problem 2
The velocity function (in meters per second) of an object moving along a line is given by
v(t) = t − 2 , 0 ≤ t ≤ 4.
(a) Find the displacement (in meters) of the object during the time interval 0 ≤ t ≤ 4.
(b) Find the distance (in meters) traveled by the object during the time interval 0 ≤ t ≤ 4.
Problem 3
This problem has two separate questions (a) and (b). Answer each question.
(a) Evaluate the definite integrals ∫ (^0)
− 6
36 − x^2 dx and
− 2
|x| dx
by interpreting them in terms of areas.
(b) Evaluate the definite integral (^) ∫ 4
1
3 x − 4 √ x
dx.
(Your answer must be a real number!)
Problem 5
This problem has two separate questions (a) and (b). Answer each question.
(a) Evaluate the indefinite integral
x^2 ex^ dx.
(b) Evaluate the indefinite integral
x − 11 (x + 1)(x − 2)
dx.
SCRATCH PAPER
(Scratch paper will not be graded!)
