Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Perform each of the following integrations.
ܐ
(a)
de
(b) / 8 si(¹)dr
(e) fsee (2) tan (2)de
(4)√9-7-de
(e)
00 / 174
inly)
-e
-sm(z)
1
29/₂
7/4
fo
=√30
te
1
éta
-S
+C
$9-x² dx
9x-X² +c
%
3 Loso 3 cosodo
- S'a cos odo
9(1-sino) do
9-9 sın²0 do =
e
514
#4
3 3
17/6
+C
"\'a\l-si •3uested9-
-√³√ cosio · 3cosodo
•√9-(9sion B)² · 3 cost de
- S. √9-9 sin³8
1-
(056) e
-5m (7)
• 3 cosodo
3²x²
9 (3) (3) - (9 (0)-7)
27
81 27
(056x) e du
2/4
17/6
SG)
D) √° √9-x² dx = ²³² √²3²-x²dx= x=a sing
x=3sing
dx= 3 cosado
-Sin(x)
dx
H
-(-esuz)
(Dety)
(= -Sin(e)
du - Cos(x)dy
h
-e +etc
08₁-26 x
SA-
u-x-3
du
cos(x)
27 = (10)
du=dx
J-du
8²-20² du
<8/n/u/ -2/+c
= $nul+2+c
= 8/n/x-31+2+3+C
--
8-16-A(x-3) +B
La let x=3
800)-26-8
ها - .
b) 8x² sin(x²) dx
2x4
=√x² Sincu) tadu
= (2xsin (u) du
=12usin Cubdu
4₂x=2
16-26-4-2
-6-4-2
2ucoscu)-S (oscu)- 2du
2u Cos(u)-2sin(u)+c
2xcos(x)-25in(x)+(
C) Secx) tan(x) dx
- sec) sec²x) tar() tan (1)adx
- sec (x) sec²(x)
du
=√ sect) ²³. du
=S (tan² (x)+1) u ²³. du
*S (u²+1) ²³. du
= Suº²+ u²³ du
=
e) | __!
+
|| 9
tan (x)
11
+C
U=X4
du=4x³dx
xdu=dx
[_A4X²-4x+1²% dx = f
W = 2u
dw=2 dv
tan (x)
9
cos cos
(1-sinto) Coso
+C
(1-1²) cost
S1-w²dw
√ (44²-44x42²72x
√((2x-1)² + 1)²
(seco)
S secours secodo
=√ se = do
(2x-1) (2x-1) +1
dx
= d
√(U²+1J5
u= tant
Justomer je é secodo duas e secado
dw
EOSO
dv=sin (4)du
V = (os (u)
W=sind
dw-cosado
= do
LOSA
W3
3
W-
let u = tan (x)
du-sec²x)dx
s dx
+c
3
**
u=2x-1
du-2dx
du=dx
2,
tan
h
h- Ju²+1²/
Sing Sino +c
3
u
Vn²tist vu²r +C
+C
(2x-1)3
3√x+1
√(2x-13² +1²²
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