Problem

If $ a $ and $ b $ are positive numbers, show tha…

View

Problem 90 Hard Difficulty

If $ f $ is continuous on $ \mathbb{R} $, prove that
$$ \int^b_a f(x + c) \, dx = \int^{b + c}_{a + c} f(x) \, dx $$
For the case where $ f(x) \ge 0 $, draw a diagram to interpret this equation geometrically as an equality of areas.

Answer

SEE GRAPH

More Answers

01:31

Frank L.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Watch More Solved Questions in Chapter 5

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

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Problem 94

Video Transcript

we know that for this question, withdrawing the diagram The first thing you could do a substitute you is expose. See, this indicates that D axe is do you? Because it's just one as the derivative of X. Therefore, in of the limits of integration, change to a pussy on the bottom and people see on the top after vax d axe Remember wise half of Expo See you had shifted by C units in the left direction horizontally after vax on the right and affects was seeing left.

Amrita B.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University