Quiz 5 - Math XXXXXXXXXX)
Instructions:
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• This quiz is due at 11:59 PM (Eastern Time) on Tuesday, November 29.
***********************
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1
Quiz 5 - Integration Techniques II
1. Chapter 8-4, Problem 6.
2. Chapter 8-4, Problem 8.
3. Evaluate the integral
∫
e2x
e2x + 3ex + 2
dx.
4. Evaluate the integral
∫
x+ 4
x2 + 2x+ 5
dx.
5. Evaluate the integral
∫
4x
x3 + x2 + x+ 1
dx.
6. Chapter 8-5, Problem 26.
7. Chapter 8-5, Problem 40.
8. Evaluate the integral
∫
x√
3− 2x− x2
dx.
9. Chapter 8-6, Problem 8.
10. Evaluate the integral
∫
sec2 x
tan2 x+ 3 tanx+ 2
dx.
2
In problems 13-36, evaluate the integrals. (More than one method works for some of the integrals.)
ao
18 SN 6? a
nfs «
2S
In problems 37-42, first complete the square, make the appropriate substitutions, and evaluate the integral
wm = wf —s
|
PROBLEMS
Evaluate the integrals. (More than one method works for some of the integrals.)
1 J ion» c JESREREIS
x
a Ein) ax so J tan ax 6 J cotton ax
0 0
86 Integrals of Trigonometric Functions. Contemporary Calculus
7. J day d 0. J anxreostrn) ax
0
10. J sncrareoin ax snes’ ny ax 12. Fn Gureoson ax
13. J snl anreoan) ax orcas’ Gr) dx
16. J eum on 17. J ed toranin a
The definite integrals of various combinations of sine and cosine on the interval [0.27] exhibit a
number of interesting patterns. For now these patterns are simply curiousites and a source of additional
problems for practice, but the patterns are very important as the foundation for an applied topic. Fourie
Series, that you may encounter in more advanced courses.
The next three problems ask you to show that the definite integral on [0.251] of sin(mx) multiplied by almost
w=
In problems 37-42.
ET
7 = !
wf a Sm x
85 Trigonometric Substitution Contemporary Calculus
Fx) =-5x—1) = + 3(x+2) ~.
£700 = 106-17 ~ 60427, and
£70 = XXXXXXXXXX
9x41
Practice 6: Use the partial fraction decomposition of g(x Fo
to calculate g(x),
£700. and g D0).
PROBLEM
In problems 1 — 12, decompose the fractions.
7x42 Tx +9 1x +25
LGD TFIG-1
Caos
224 15x +25 6x24 9x15
From XEFHE-1
82 x43 9x24 13x4 15
10.
Coax X42" 3x
In problems XXXXXXXXXX, evaluate the integrals.
3x4 13 2x4 11
so feats ou oy we
J alyomea
Fax
16. ax 17. Integrate the functions in problems 1-4.
1
Integrate the functions in problems 5 - 8
XXXXXXXXXX19x 4
a 0, [BFR
exon rents
af 3419x424
ax