636 Solutions to exercises
47.neither:
even: ;
odd:
Section 5.4
48.πab 49. 61254
Section 5.6
- (i) 1 (ii) 66 (iii) 60
- (i)l
3
23 (ii) l
2
23 (iii) 3 l 24
(iv)l
5
251 − 1 x
0
l
4
221 + 1 x
0
2
l
3
23 (v)l
5
280
Section 5.7
(i) 1 (ii) 7 (iii) 37
(i) (ii) (a)
(b)
- (i) (ii) (a) (b)
Section 5.8
- (i)p(V
2
1 − 1 V
1
)
(ii)
Chapter 6
Section 6.2
- 0 9.
−
- 0 9.
2
3
π
4
1
42
(sin 3773 xxC++sin )
1
8
(sin sin )22 4xxC−+
1
8
(cos cos )22 4xxC−+
−++
1
10
(cos 55 xxCcos )
−+
1
12
cos 6 xC
1
12
(sin) 66 xxC−+
nRT
Vnb
Vnb
na
VV
ln
2
1
2
12
11
−
−
−−
1
2
1
2
kx()−
1
2
k
1
2
2
kx
1
2
1
2
kx()−
−
1
2
k
−1
2
2
kx
1
2
22
kx x()
BA
−
1
2
31
2
()()()xeexee
xx xx+−++
−−
1
2
31
2
()()()xeexee
xx xx+++−
−−
Section 6.3
21.ln(x
2
1 + 1 x 1 + 1 2) 1 + 1 C
23.−ln(1 1 − 1 sin 1 x) 1 + 1 C 24.−ln(cos 1 x) 1 + 1 C
26.−ln[ln(cos 1 x)] 1 + 1 C
28.cos[1 1 − 1 ln(cos 1 x)] 1 + 1 C
34.− 4 35. 36. 37.
Section 6.4
40.−x 1 cos 1 x 1 + 1 sin 1 x 1 + 1 C
41.3(x
2
1 − 1 2) 1 sin 1 x 1 − 1 x(x
2
1 − 1 6) 1 cos 1 x 1 + 1 C
- 1
- −
1
9
−
lnx
x
C
1
x
xC
2
4
(ln ) 21 −+
1
4
1
4
221
22
()xxeC
x−+ +
−+
1
4
sin 2 xC
1
2
12
1
2
12
2
()sin ()cosxxxx+++
T
rΘ
1
2
1
2
π
4
2
3
1
6
ln 10
21
xxC−
−
tan
1
2
1
12
sin
−
−−
xx x C+
1
22
1
tan
−
x
C
1
4
4
sin xC+
−− + 4
2
xC
1
2
23
32
ln(xx C−++)
1
6
31
2
sin(xC−+)
2
3
1
32
()++eC
x1
2
2
eC
sinx+
−− +1
3
4
232
()xC
1
4
42
2eC
xx−−+ +
−+
eC
()xx321
4
231
343
()xx C+− +
1
8
325
24
()xx C++ +
1
3
21
32
()xC−+
1
18
31
6
()xC++