Problem

Which of the following integrals are improper? Wh…

01:32

Problem 1 Easy Difficulty

Explain why each of the following integrals is improper.

(a) $ \displaystyle \int_1^2 \frac{x}{x - 1}\ dx $
(b) $ \displaystyle \int_0^\infty \frac{1}{1 + x^3}\ dx $
(c) $ \displaystyle \int_{-\infty}^\infty x^2 e^{-x^2}\ dx $
(d) $ \displaystyle \int_0^{\frac{\pi}{4}} \cot x\ dx $

Answer

a. Type 2 improper integral.
b. improper integral of Type 1.
c. improper integral of Type 1.
d. Type 2 improper integral.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Video Transcript

explain why each was a falling into growth is improper. So before we do this problem that record the definition of improper into girls, well functions are fives into grow off our backs. May Toby is improper. If Interpol a Toby is infinite or a fax has infinite this continue t r a to B. Now let's do the problem. B and C Interval. It's infinite. So they're improper into girls. For a what axe goes to one. A function acts over X minus one Cost if infinity because two nominator cost to zero So dysfunction has infinite. Did this continue? T I want to. So it is improper, integral. And for the axe goes to zero Potanin axe goes to infinity. So the function have contended acts has infinite this continuing on their own to pile of or so it is improper integral

WZ

Wen Z.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Top Calculus 2 / BC Educators

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University