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MA 126-7B, CALCULUS II
October 11, 2010
Name (Print last name first):..........................................
Student Signature:...................................................
TEST II
Closed book test – No calculators are permitted!
PART I
Each question is worth 5 points.
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!
Question 1
If
0
f (x) dx = 4 and
0
g(x) dx = −2, find the numerical value of
0
(f (x) − 5 g(x)) dx.
Answer:.....................
Question 2
Find the derivative of the function g(x) =
x
2
ln(
t) dt.
Answer:.....................
Question 3
Evaluate the definite integral ∫ (^) e
1
x
dx
(Your answer must be a real number!)
Answer:..................
Question 4
Evaluate the definite integral
∫ √π
0
2 x sin
x 2
dx. (Your answer must be a real number!)
Answer:..................
Question 5
Evaluate the indefinite integral
xe x dx.
Answer:..................
Question 6
If r(t) = < t 2 , cos(t), sin(t) >, find the tangent vector r ′ (t) when t = 0.
Answer:..................
Problem 2
The velocity function (in miles per second) of an object moving along a line is given by
v(t) = t
2
(a) Find the displacement (in miles) of the object during the given time interval 0 ≤ t ≤ 2.
(b) Find the distance (in miles) traveled by the object during the given time interval
0 ≤ t ≤ 2.
(Simplify and express your answer as a fraction if need be!)
Problem 3
This problem has two separate questions (a) and (b). Answer each question.
(a) Evaluate the definite integrals
− 3
9 − x^2 dx and
− 1
|x| dx
by interpreting them in terms of areas.
(b) Evaluate the indefinite integral
∫ 1
x
ln(x)
dx.
Problem 5
This problem has two separate questions (a) and (b). Answer each question.
(a) Evaluate the indefinite integral
x 3
x
x^2
dx.
(b) Evaluate the definite integral
0
x^2 + 4x + 3
dx.
(Simplify your result by expressing your final answer as a single logarithm!)
SCRATCH PAPER
