Problem

Evaluate each integral. $$ \int_{1}^{5} y e^{4 …

Problem 9 Easy Difficulty

Evaluate each integral.
$$
\int_{0}^{3} y e^{4 x+y^{2}} d y
$$

Answer

$\frac{1}{2}\left(e^{4 x+9}-e^{4 x}\right)$

Topics

Multiple Integrals

Functions of Several Variables

Book Cover for Finite Mathematics …

Finite Mathematics and Calculus with Applications

Chapter 17

Multivariable Calculus

Section 6

Double Integrals

Discussion

You must be signed in to discuss.

Top Calculus 3 Educators

Lily A.

Johns Hopkins University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Watch More Solved Questions in Chapter 17

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

{'transcript': "amongst this to take the definite integral from 0 to 3 of wine times the, uh, to the floor ax. Plus. Why square with respect to why? To do this, I'm gonna cover to the Sunday of some use substitution. So you is equal to four x plus. Why square and the derivative of you with respect to why it's just gonna be to I d y. Okay, so in order to put it to in here, I'm gonna multiply the inside, but to the outside about 1/2 okay. To get our do you in there. So now we can write this expression as 1/2 definitely go from 0 to 3 of e to the year. Deal. Okay. And the integral of either the you do you is just eight to the U. So we're gonna evaluate one house times uh, eat of the year, Uh, from 0 to 3. Okay. So, uh, maybe I could do this in, so we're gonna have 1/2 times he to the and then plugging. And three, we're gonna have four x plus nine. Never in its a try and P to the for X plus zero. Okay, So you she might be able to simplify this now. Previously like that to Yeah, that's that's it. So there's your definite integral from 0 to 3 of the infection. Use amuse substitution for it. Thank you very much."}

CC

Charles C.

Kennesaw State University

Topics

Multiple Integrals

Functions of Several Variables

Book Cover for Finite Mathematics …

Finite Mathematics and Calculus with Applications

Chapter 17

Multivariable Calculus

Section 6

Double Integrals

Top Calculus 3 Educators

Lily A.

Johns Hopkins University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor