Improper Integrals Questions here are some calculus 1 integration questions, i want a clear solution for those questions only: problem 26 and 13 in page 3
Improper Integrals Questions here are some calculus 1 integration questions, i want a clear solution for those questions only:
problem 26 and 13 in page 333
problem 7a and 13a in page 350
problem 74 and 67 in page 352
42 and 41 in page 372
19 and 6 and 3 in page 459
48 and 9 in page 466
19 and 15 and 5 and 1 in page 479
13 in page 505
i don’t just want solution, i also want explanation for the steps and how you find the answer
i don’t mind handwritten, just make it clear
thank you. Question 1, 5, 15, 19 – Page 479
Exercises 8.4
19.1
20.
Expand the quotients in Exercises 1 & by partial fractions.
58
7
1.
2.
X’d
Der + 2x 1)
.
22
s Excises 2.pies the marad as a sum di parwal fractions
and evaluate the integrals
3.
4.
Y
S.
.
ix + 1) re 1
24-11
2 2,41
8
.
24.
I
7.
8
2.2
as
26.
ds
Nonrepeated Linear factors
In Exercises 0.16, express the integrand as a sun of partial fractions
and evaluate the integrals.
2.
28.
dx
1
31
11.
fr
6
12.
RM 5
1
13.
14.
du
3
15. /
16.
Ä®
21
Question 13- Page 505
Evaluating Improper Integrals
Evaluate the intcgrals in Exercises 1-34 without using tables.
41.
SIN/
de
1.
dx
2
42.
X
(Hint: 1 sin / for 1 0)
su!
4.
ih
VY
43.
1
dx
1 – Y
1
dx
5.
2. /
”
[
I
L
6.
45.
46.
.
3. [”
La
7. Ivi
9. |
1.
Jo
5.
🙂
–x In x|dx
8.
ch
0
47.
48.
2 db
9.
2 dx
dv
9.
50.
1
2
du
2 di
12.
d
ch
V
52.
2x dx
13.
14.
x x
+ 4)2
53.
x dx
54. .
15.
16.
Sot
ds
55.
2-COS X
VA-28
1 + sin
Cos* dx
So
:
56.
[?
A
dx
(1+r) VX
f
[
17.
18.
2 di
dx
57.
rV
58.
1
dx
In x
1
Question 3, 6, 19 – Page 459
Integration by Parts
Evaluate the integrals in Exercises 1-24 using integration by parts,
15.
fred
16.
1.
1.
xsin adx
2.
A COST do
17.
(?
Sier
18.
(
refer you are the le’ dr
pie
1
Vre
✓
3.
1
4.
X
Sinxslar
19.
redy
20.
✓
1
5.
* In xdx
x Inrdx
21.
sin i de
22.
h
rele
(?cos y di
7.
./
1
6. /
./
..]
I
1
8.
Ver
23.
COS 3rd
24.
sin 2x dx
9.
10.
ir – 2.8 –
Dex
Using Substitubon
Evaluate the integrals in Exercises 25-30 by using a substitution prior
to integration by parts.
11.
tan ‘ydi
12.
sin var
1
I
13.
secdi
14.
4x sec+ 2x dx
25.
V3x*
26. /
XVI – xdx
Question 9, 48 – Page 466
Powers of Sines and Cosines
Evaluate the integrals in Exercises 1 22.
Powers of Tangents and Secants
Evaluate the integrals in Exercises 33 50.
1.
Cox 2.3 cr
2.
/
och
Stand
34
1
Sec tan td
3.
cos x sin da
sin 2x cos 2x d
./
🙂
1
1
35.
1
I
. 1
Ä‘Y :1th : tt
I see’s
Y tán
1
5
sin’x x
6.
7.
sind
37.
sce” x tan- x x
8.
1
sinds
sec**tan” x d
9.
cos’
.
39.
. [ 2 seede
e seca
sin roosid
12.
1
cos 2x sin 2x x
1
42.
1.
1
1
3 sec 3xxir
cos’xd
.
cscto do
secret
15.
sin de
16.
7 cos di
45.
46.
f
6 tand
8 sin* x dy
1
I
[
8 cost28
tan’da
48.
cot 2:
19.
16 sin .xcosas de
20.
8 sin”, cosa y de
49.
***dx
f
50.
1.1
8 cotid
21.
1 800
8 cos 20 sin 2018
22.
sin 20 cos
Question 74, 67 – Page 352
Find the areas of the regions enclosed by the lines and curves in Exer-
cises 63.72.
63. y
x?
and
2
x and
65.
.
and
81
66. = x
and
1
VANA
pa and
2×2 and
68.
**4
and
70.
j
x Va
and
71. = Vand Sy mr 6 (How many intersection points
are there?)
72. y –
and (1/2) + 4
Find the areas of the regions enclosed by the lines and curves in Exer-
cises 73 80.
27. 0. and
74. I
y and
X + 2
75. 12
and
16
ya
0 and x + 2y? 3
77. r ty? 0 and
1+ 372 2
0 and
79.
1 and MV1 – 12
73. X
.
er.
76. 1
78. 1
w
X
Question 41, 42 – Page 372
Find the volumes of the solids generated by revolving the regions
bounded by the lines and curves in Exercises 39.44 about the .r-axis.
39. V = x,
1. = 0
= 2V1.
41. x + 1.
42. = 4-1, 1 = 2-X
1= V2, -7/4 S rs74
w Sect.
44, P = sec x.
tant,
In Exercises 45-48. find the volume of the solid generated by revolv-
ing each region about the jo-axis,
45. The region enclosed by the triangle with vertices (1.0), (2.1). and
(1.1)
46. The region enclosed by the triangle with vertices (0,1).(1.0), and
(1.1)
47. The region in the first quadrant bounded above by the parabola
y=x. below by the x-axis. and on the right by the line x = 2
Question 13, 26 – Page 333
Evaluating Integrals
Evaluate the integrals in Exercises 1-34.
23.
23.
24.
+ 1)(2-2)
3
1.
(2r
3) dr
2. 15
🙂
dy
sin 2x
26.
(cos.r + sec.x) dx
2 sm x
3.
3.1.
S
lo
100
1*(4—)di
w
3) dr
4. I
(x?
2x – 3) dx
27.
28.
(cosx + cos x) dx
A
T
5.
3.x
– 2x – 3) dr
* + 3)
29.
30.
4
1:2
4
7.
VR) dx
8.
31.
ar
32.
dx
4×2
x
dx
VI
6. /
”
le
To
ch
1
33. [.
».
dr
fi
9.
2 secx dx
10.
(1 Cosy) ds
11.
csc o coto do
12.
4 sec utan u du
In Exercises 35 38. guess an antiderivative for the integrand function.
Validate your guess by differentiation and then evaluate the given def-
inite integral. (Hint: Keep in mind the Chain Rule in guessing an anti-
derivative. You will learn how to find such antiderivatives in the next
Section)
13.
1 + cos21
di
2
14.
-COS 27
2
35.
te
36.
Jo
5.
tan- x dx
15.
Si
10.
iseer i tan .x) il
xdi
(93
6X
}
Question 7a, 13a – Page 350
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1*
the Substitution Fernilai lheurem tule the materia
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है
3
21
1938
2
BL 3003 x sila cis
0)
in
ww
3
* !
La
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+
f
1
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