Problem

Evaluate each definite integral. $$\int_{1}^{4} …

02:19

Problem 13 Easy Difficulty

Evaluate each definite integral.
$$\int_{1}^{4} \frac{3}{(3 x+2)^{2}} d x$$

Answer

$\frac{9}{70}$

Topics

Integrals

Integration

Integration Techniques

Book Cover for Calculus with Appli…

Calculus with Applications

Chapter 7

Integration

Section 4

The Fundamental Theorem of Calculus

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

GH

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

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

Video Transcript

problem. 13 were asked to find this definite in and to do this problem, since it's has, since it has a fraction and a function inside of the function where we're gonna use U substitution and let you equal three X Plus two and we choose this for you because it's a function inside of a square. So if you find the derivative of both sides, you get three d ETS. And this comes out handy because we have a three D X in our originally kitchen so we can go ahead and write this. But before doing that, we have to notice that we have bounds and in the bounds these air expounds We have changed them too. Why bound? And to do that, we just plug it into this equation who, 33 times before plus two to find the upper bound and to find the lower bound we would do three times one plus two. So the upper round is 14 and the lower bound is five. And now we can do the U substitution so would be won over you squared times the u. So this equals you to the minus one over. Now get a one. And you would evaluate this from I to 14. So that just means you have to plug in 14 in replacement of you and then minus Have to plug in five in replacement of you. And this gives us one over 14 minus one word. Negative five. Is this nine over 70?

Aishwarya K.

University of Southern California

Topics

Integrals

Integration

Integration Techniques

Book Cover for Calculus with Appli…

Calculus with Applications

Chapter 7

Integration

Section 4

The Fundamental Theorem of Calculus

Top Calculus 2 / BC Educators

GH

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham