Math 1342 – Calc 2 – Homework Chapter XXXXXXXXXXNAME:________________ Math 1342 – Calc 2 – Homework Chapter XXXXXXXXXXNAME:________________ §4.1 Approximating Polynomials #1-3, 7-11, 15, 16, 20 Math...

Math 1342 – Calc 2 – Homework Chapter 2.5 NAME: ________________
Evaluate the integral if it converges; otherwise, show that the integral diverges.
(
)
(
)
(
)
1/2
1
2
1
1
1
4.
4y-3
Solution:
Let 43
On differentiating both sides, we get
42
2
At 11 and at
Now, the integral can be written as,
1
2
1
2
1
2
Hence, the integral
dy
yt
tdt
dytdtdy
ytyt
tdt
t
dt
t
¥
¥
¥
¥
-=
=Þ=
=Þ==¥Þ=¥
æö
ç÷
èø
=
==¥
ò
ò
ò
diverges.
0
0
0
5.sin
Solution:
sin cos|
cos0cos
therefore, the integral diverges.
zdz
zdzz
¥
¥
¥
=-
=-¥=-¥
ò
ò
(
)
[
]
2
0
2
1
1
0
2
9.
1
=arcsin()| Using,
a

1
rcsin(1)arcsin(0)
0
2

dx
arcsi
x
dt
t
t
nxC
pp
=+
-
=
-
æ
æ
è
ö
ç
ç
÷
èø
-
ö
=-=
÷
ø
ò
ò
(
)
2
0
2
2
0
0
.
10.
arct
2
a
1
1
lim
1
=lim[arctan(t)] Using,
=lim[arctan(b)-arctan(0)]
=
Hence, the integral conver
n ...