homework5 - 31B Homework 5- Due Friday, May 10th in class...

31B Homework 5- Due Friday, May 10th in class
Uncollected problems:
Section 8.6 # 5, 6, 11, 20, 21, 27, 29, 37, 40, 43, 47, 59, 64, 67, 77, 81
Section 8.8 # 7, 10, 15, 31, 33, 35, 44, 53
Collected problems:
1. Integrate the following improper integrals:
(a)
Z
1
0
x ln( x ) dx
(b)
Z
∞
-∞
x
3
e
- x
4
dx
2. Determine if the following integrals converge or diverge:
(a)
Z
∞
1
7 cos
2
( x )
3 + x 2
dx
(b)
Z
π/ 2
0
2
x sin( x )
dx
(c)
Z
∞
1
2
√
4 x
2
- 2
dx
3. In this problem we will approximate the integral of cos( x
3
) over the interval [0 , 2].
(a) Write an expression for M
N
, T
N
and S
N
with N = 4.
(b) For each of the approximations determine an