Math 1210
Quiz 9
March 28th, 2014
Answer the following three (3) questions. The value of every question is
indicated at the beginning of it. You may use scratch paper, but you can
only turn in this sheet. Please write your answer in the space provided. You
have 20 minutes.
Name:
1. (10 points) Consider the function f (x) =
UID:
Rx
0
cos(u) du over the interval [0, 2π].
(i) (5 points) Find f 0 (x) and f 00 (x).
(ii) (5 points) Over which intervals is f (x) is increasing (resp. decreasing)?
2. (10 points) Consider the function f (x) =
R cos x
sin x
t3 dt
(i) (4 points) Compute f ( π4 ) and f (0).
(ii) (6 points) Find f 0 (x).
Ra
R cos x
Hint: Write f (x) = sin x t3 dt + a t3 dt.
3.
(i) (6 points) Compute the indefinite integral
√
Z
x sin x2 + 4
√
dx
x2 + 4
Hint: Use the change of variables u =
√
x2 + 4.
(ii) (4 points) Compute the definite integral
√
Z 1
x sin x2 + 4
√
dx
x2 + 4
0
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