Quiz 4 - Math XXXXXXXXXX)
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1
Quiz 4 - Integration Techniques I
1. Chapter 8-1, Problem 2.
2. Chapter 8-1, Problem 8.
3. Chapter 8-1, Problem 18.
4. Chapter 8-1, Problem 30.
5. Chapter 8-2, Problem 44.
6. Chapter 8-2, Problem 50.
7. Evaluate the integral
∫
e2t cos(3t) dt.
8. Chapter 8-3, Problem 36.
9. Evaluate the integral
∫ √3
1
arctan
(1
x
)
dx.
10. Using integration by parts, calculate
∫ √π
√
π/2
x3 cos(x2) dx.
2
x-axis for x 2 1 and the graph of 10) = S52
(Fig. 12) is revolved about the x-axis.
(@ The volume obtained when the area between the
positive x-axis (x20) and the graph of
1
0 = 777 (Fig. 13a) i revolved about the x-axis.
(b) The volume obtained when the area between the positive x-axis (x20) and the graph of
1
0 = 77,7 (Fig. 130) is revolved about the y-axis. (Use the method of “tubes from section 5.5)
XXXXXXXXXXThe volume obtained when the area between the positive x-axis (x20) and the graph of
1
x)= is revolved about the x-axis.
PY kX)
e]
xeln(x)
Contemporary Calculus
incon nnd 27 wos
o
.
:
Example 30) showed hat J ds. grew abivarily large a C grew abil lrg, so fn
1
amount of paint would cover the area bounded between the x-axis and the graph of f(x) = Ix for x
1 (Fig XXXXXXXXXXShow that the volume obiained when the area in Fig. 11 is revolved abou the
2]
J wean a
ow Jeenta
In problems XXXXXXXXXX, complete the square in the denominator, make the appropriate substitution, and integrate.
ofr wf —w is
Tram
1 3
a6 J —a a. J—=—
S20 10 Fr10:+29
dx 4.
In problems 49 — 54, evaluate the first integral as a sum of two integrals.
20411
ares
axa 448
50 Jp a ft de Iris
ax =
. er of ae fw
Zoersto MTT Taino © orto
Jw
Ere
Imire
y
ax=9 J dr ax. wernow fz ox isdivergem
1x 1*
ythe P-Test = 12.1), 50 we cam conclude that J 2 an is ivergent.
s
In 1-21, use the definition of an improper integral o evaluate the given integral.
Ike Jt yi
Lwin? J Lex
, xine)
Contempo