Problem

Although it is often true that a double integral …

07:54

Problem 36 Easy Difficulty

Find the volume under the given surface $z=f(x, y)$ and above the rectangle with the given boundaries.
$$z=e^{x+y} ; 0 \leq x \leq 1.0 \leq y \leq 1$$

Answer

$e^{2}-2 e+1$ cubic units.

Topics

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Book Cover for Calculus with Appli…

Calculus with Applications

Chapter 9

Multivariable Calculus

Section 6

Double Integrals

Discussion

You must be signed in to discuss.

Top Calculus 3 Educators

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 9

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

Video Transcript

Okay, Another volume problem. So instead of our double integral x and Y are both going from zero to one in a grand A Z to the explosive all high So this is a supersymmetric and a girl I'Ll just put the eggs first of the matter Get on the wife first, Ok? And so anti derivative here. Well, it's just it's stuff. I mean, this is just about as easy as it gets. Justine, evaluate zero to one value extra zero one. So that's just okay. Me too. The one plus why minus c to the y. Okay. And then this is pretty straight forward again. Anti derivatives or just the exponential is themselves. You won. Okay, so if we evaluate at one will get he squared minus a and then minus evaluated zero. Me too. The one minus one. So what is that? He squared minus two e Plus, what

Matt J.

Georgia Southern University

Topics

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Book Cover for Calculus with Appli…

Calculus with Applications

Chapter 9

Multivariable Calculus

Section 6

Double Integrals

Top Calculus 3 Educators

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University