Problem

Evaluate the integral. $ \displaystyle \int \f…

03:52

Problem 81 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int \sqrt{1 - \sin x}\ dx $

Answer

$$2 \sqrt{1+\sin x}+C$$

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Samuel H.

University of Nottingham

Joseph L.

Boston College

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

Problem 83

Problem 84

Video Transcript

let's start here by taking you use up. Let's take you to just be sign of X, then do you that she's co sign X t X And now the difficulty here will be t just free. Write this in terms of you because we would liketo have d x by itself here. That means we would liketo have something like this, but not quite because yes, we do have the X by itself. But the left side has a u an ex so have to rewrite this in terms of you. So we know that co signs where is one minus science where and then just take a sweet room here and then using our use up. This is one minus, you swear. So let's do do you over one minus you square equals DX. So now rewriting on Integral This is square rule of one minus you up top and then for DX we have do you and then over one minus is where? Oops! Next. Let me just go ahead and simplified that denominator. Who's that? Should not be swearing there as he won mine issue of talk. Then the bottom have one minus you and then one plus you after factoring and then just splitting the radical of over the private. So all I did there was just use the fact that he multiplied two positives in the radical We can write this and then I could go ahead and cross off those terms there er and purchase left over with do you over the square of one. Plus you. Now this is much simpler, integral than what we started with. So for this one, you could do it. Another use of here, Let's go to the next page. This time let's take me to be one plus you So that D v equals to you that we could write this in a girl as one over Rudy Davey. So if we want was to be to the negative one half. So that's to be two the one half. Plus, he go ahead and replace G with you coming from our second use of up here and then recall the original use of on page one was signed X. So now we come back over here and replace that you with sine X, and that's our final answer

JH

J H.

Topics

Integration Techniques

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Samuel H.

University of Nottingham

Joseph L.

Boston College