Problem

Evaluate the integral by interpreting it in terms…

02:43

Problem 37 Hard Difficulty

Evaluate the integral by interpreting it in terms of areas.

$ \displaystyle \int^0_{-3} \bigl( 1 + \sqrt{9 - x^2} \bigr) \, dx $

Answer

$$3+\frac{9}{4} \pi$$

Maya R.

November 26, 2021

Very well explained, thank you.

Top Calculus 1 / AB Educators

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

Video Transcript

in order to evaluate this under girl here, we could first graft dysfunction. And to do so, we could actually just graph this nine minus sex weird, which is a circle. And then it shifted up one. And therefore it has a radius three, but then shifted up one unit and therefore it has a Y intercept up for So basically, from here below, we just have a big rectangle and that indicates how much it shifted. Now we want to find the area from negative 3 to 0. So we want to find this area as well as the area of the semi circle. So let's just start with the rectangle. Well, that's just the height of one width of three and therefore that has in the area of three. They're positive. And then what about thesis Urkal? The area for a circle is pi r squared. So it's just write that x squared our radius. And this case is three so deep I times three square. But then we're only interested in 1/4 of it the circle. So it's over four or another way to rewrite that is nine pie sports. That is the area of this top region here. So adding those two together, we would get that the Senate girl evaluates to using geometry three plus nine high over four. And we could just go ahead and leave this because this is our exact answer.

Stephen H.

University of Utah

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 2

The Definite Integral

Problem