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MA 126-6A, CALCULUS II
October 17, 2007
Name (Print last name first):..........................................
Student ID Number (last four digits):........................
TEST II
Closed book test – No calculators are permitted!
PART I - Basic Skills
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 = −20 and
8
f (x) dx = −35, find the numerical value of
0
f (x) dx.
Answer:.....................
Question 2
Find the derivative of the function g(x) =
∫ (^) x
1
sin (t^3 ) dt.
Answer:.....................
Question 3
Evaluate the definite integral (^) ∫ e
1
x dx
(Your answer must be a real number!)
Answer:..................
Question 4
Evaluate the indefinite integral
1 + x^2
dx.
Answer:..................
Question 5
Evaluate the indefinite integral
sin x cos x dx.
Answer:..................
Question 6
Evaluate the definite integral
0
xex^ dx. (Your answer must be a real number!)
Answer:..................
Problem 2
Consider the function f (x) = (x − 1)^2 on the interval [1, 4].
(a) Find the average value, fave, of the function f on the given interval.
(b) Find the numerical value of c such that fave = f (c). [Hint: only one value lies in the given interval!]
Problem 3
(a) Evaluate the definite integral ∫ (^2)
1
3 x^3 + 2x^2 + x x dx.
(b) Evaluate the indefinite integral
x ln x dx.
Problem 5
(a) Evaluate the indefinite integral (^) ∫ x^2 cos x dx.
(b) Find the exact area of the region between the graph of the function f (x) = 2xe−x^2 and the x-axis when 0 ≤ x ≤ 1. (Hint: Substitution method might prove useful here!)
SCRATCH PAPER
