MATH 101 HOMEWORK 7
Due on Wednesday Nov. 10, 2004.
For full credit, show all work. Calculators are not allowed, except as indicated below.
1. (5 marks) The speedometer reading (v) on a car was observed through a 10-minute
period at 1-minute intervals and recorded in the table below. Use Simpson’s Rule to
estimate the distance travelled by the car. (The total distance travelled is the integral
of the velocity. All readings are in kilometers per hour. In this problem, you may use a
calculator.)
t
0
1
2
3
4
5
6
7
8
9
10
v
56
58
62
61
64
66
63
60
61
63
61
2.
Z ∞(5 marks) We
dx
√
, but
1 + x6
1
Use a substitution
on page 398 of the
want to use a numerical method (eg. Simpson’s Rule) to evaluate
we can’t do it directly because the interval of integration is infinite.
to convert this integral to one over a finite interval (see the examples
textbook).
3. (10 marks) Calculate the volume of each solid, using either slices or cylindrical shells,
whichever you prefer:
(a) The solid generated by rotating about the x-axis the region bounded by the curves
y = cos x, y = sin x, and the lines x = 0, x = π/4.
(b) The solid generated by rotating about the y-axis the region bounded by the curve
y = ex , and the lines x = 1, y = 1.
This homework covers Sections 6.7–6.8 and 7.1 of the textbook. Additional recommended
exercises: Section 6.7: 1–10; Section 6.8: 1–9; Section 7.1: 1–23.
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