Problem

Evaluate the integral. $ \displaystyle \int^{…

02:05

Problem 33 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int^{2}_{1} \biggl( \frac{x}{2} - \frac{2}{x}\biggr) \,dx $

Answer

$$\frac{3}{4}-2 \ln 2$$

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

Video Transcript

were asked to the integral from 1 to 2 of X over two, but divided by two is the same thing is multiplied by one half. So that's what I would leave that as -2 over X. Whatever works for you. Um But I would do this because then when I'm looking at the anti derivative and I add one to the exponents. You know, I'm looking at The exponents now to the second power and then multiply by the reciprocal will half times half is 1/4. Now looking at the next one, I just haven't memorized and a lot of people know that when it's one over X, the anti directive is natural log but you can work it out if you tried your power rule and add one to the expo you'd be divided by zero. So that's an issue. And we're doing our bounds from 1-2. Well now we can plug in our upper bounds, Well two squared is four and 1 4th of four is 1 -2. Natural log of two and then minus your lower bound, which is one plugged in for each of these. Well one squared is once we're looking at 1/4 -2 Natural Log of one. And I expect my sister know that natural log of one is zero, so two times zero is just zero, so that's gone. Um and then from here you just might want to reduce like 1 -1 4th is three. Force when you combine them, combining this term with this term and just leave this alone and you're fine. There's nothing left to do. This is a perfect answer.

Gregory H.

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Problem