MATH 101 HOMEWORK 6
Due on Wednesday Oct. 27, 2004.
For full credit, show all work. Calculators are not allowed, except as indicated below.
1. (8 marks) Evaluate the integrals, or show that they diverge:
Z ∞
ln x
(a)
dx,
x3
1
Z 1
ln x
√ .
(b)
x
0
2. (8 marks) Use the comparison test to decide whether the following improper integrals
are convergent. Justify your answer.
Z 2
2 − sin x
(a)
dx,
2−x
0
Z π
dx
√
(b)
.
sin x
0
R1
3. (4 marks) Write out the midpoint approximation Mn to the integral 0 sin(x2 )dx. If
we want the error to be no greater than .001, how large should n be? In this problem, you
may use a calculator.
This homework covers Sections 6.5–6.6 of the textbook. Additional recommended exercises:
Section 6.5: 1–41; Section 6.6: 1–11.
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