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practice questions on improper integrals, Exercises of Applied Mathematics

Maharishi Dayanand UniversityApplied Mathematics

questions on imprper intergrals

Typology: Exercises

2018/2019

Uploaded on 12/18/2019

chandan-kumal
chandan-kumal ๐Ÿ‡ฎ๐Ÿ‡ณ

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Lecture Notes Improper Integrals page 1
Sample Problems
1.
1
Z1
1
x4dx
2.
1
Z1
1
xdx
3.
1
Z10
1
xln xdx
4.
1
Z0
e๎˜€5xdx
5.
1
Z0
xe๎˜€x2dx
6.
1
Z0
xe๎˜€5xdx
7.
1
Z
๎˜€1
1
1 + x2dx
8.
1
Z0
1
xdx
9.
1
Z0
1
pxdx
10.
1
Z0
ln x dx
11.
4
Z
๎˜€1
x
x2๎˜€9dx
12.
25
Z0
1
pxdx
13.
2
Z1
1
p2๎˜€xdx
14.
5
Z0
1
3
p2๎˜€xdx
Practice Problems
1.
1
Z1
1
xdx
2.
1
Z1
1
x2dx
3.
1
Z2
e๎˜€5xdx
4.
1
Z0
1
xdx
5.
1
Z0
1
x2dx
6.
1
Z0
1
3
pxdx
7.
1
Z5
1
xln xdx
8.
1
Z0
1
xln xdx
9.
1
Z0
xe๎˜€2xdx
10.
2
Z1
x2
x3๎˜€8dx
11.
1
Z1
1
x2+ 3 dx
12.
๎˜™=2
Z0
tan x dx
13.
1
Z0
1
p1๎˜€x2dx
14.
1
Z0
x
p1๎˜€x2dx
15.
2
Z1
1
xpx2๎˜€1dx
16.
1
Z2
1
xpx2๎˜€1dx
17.
2
Z1
1
(x๎˜€1) (x2+ 1) dx
18.
1
Z2
1
(x๎˜€1) (x2+ 1) dx
19.
1
Z0
1
3
pxdx
c
๎˜Hidegkuti, Powell, 2009 Last revised: August 24, 2013
pf2

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Lecture Notes Improper Integrals page 1

Sample Problems

Z^1

1

x^4 dx

Z^1

1

x

dx

Z^1

10

x ln x dx

Z^1

0

e^5 x^ dx

Z^1

0

xex^2 dx

Z^1

0

xe^5 x^ dx

Z^1

1 + x^2 dx

Z^1

0

x dx

Z^1

0

p^1 x

dx

Z^1

0

ln x dx

Z^4

1

x x^2 9

dx

Z^25

0

p^1 x

dx

Z^2

1

p^1 2 x

dx

Z^5

0

p (^32) x dx

Practice Problems

Z^1

1

x dx

Z^1

1

x^2

dx

Z^1

2

e^5 x^ dx

Z^1

0

x

dx

Z^1

0

x^2

dx

Z^1

0

p (^3) x dx

Z^1

5

x ln x dx

Z^1

0

x ln x dx

Z^1

0

xe^2 x^ dx

Z^2

1

x^2 x^3 8

dx

Z^1

1

x^2 + 3 dx

=Z 2

0

tan x dx

Z^1

0

p 1 x^2

dx

Z^1

0

p^ x 1 x^2

dx

Z^2

1

x

p x^2 1

dx

Z^1

2

x

p x^2 1

dx

Z^2

1

(x 1) (x^2 + 1)

dx

Z^1

2

(x 1) (x^2 + 1) dx

Z^1

0

p (^3) x dx

c Hidegkuti, Powell, 2009 Last revised: August 24, 2013

Lecture Notes Improper Integrals page 2

Answers - Sample Problems

11.) unde ned 12.) 10 13.) 2 14.) 3 2

p 3 9 3

p 4

Answers - Practice Problems

5 e^10 4.)^1 5.)^1 6.)^

2 7.)^1 8.)^ 1^ 9.)^

4 10.)^

p 3 9

ln 5  4

+^1

tan^1 2  0 :170 535 7 19.) 3 2

c Hidegkuti, Powell, 2009 Last revised: August 24, 2013