WORKSHEET 36  Fall 1995
1. Compute
Z
π/
2

π/
2
sin(3
x
)cos(5
x
)
dx.
2. It is known that
m
parts (by weight) of chemical A combine with
n
parts of chemical B to produce
a comound C. Suppose that the rate at which C is produced varies directly with the product of the
amounts of A and B present at that instant. Find the amount of C produced in
t
minutes from an
intitial mixing of
A
0
pounds of A with
B
0
pounds of B, given that
a)
n
=
m
,
A
0
=
B
0
.and
A
0
pounds of C are produced in the ±rst minute.
b)
n
=
m
,
A
0
=
1
2
B
0
.and
A
0
pounds of C are produced in the ±rst minute.
c)
n
6
=
m
,
A
0
=
B
0
.and
A
0
pounds of C are produced in the ±rst minute.
3. Find the fallacy in the following argument that 0 = 1.
u
=
1
x
du
=
−
1
x
2
dx
dv
=
dx
v
=
x
So integration by parts applied to
R
1
/x dx
yields:
0+
Z
dx
x
=
±
1
x
²
x
−
Z
±
−
1
x
2
²
xdx
=1+
Z
dx
x.
Thus 0 = 1.
4. Compute
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
 Spring '08
 Grether

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