Enroll in one of our FREE online STEM bootcamps. Join today and start acing your classes!View Bootcamps

Georgia Southern University

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 48

Use the region $R$ with the indicated boundaries to evaluate each double integral.

$$\iint_{R}(2 x+6 y) d y d x ; \quad 2 \leq x \leq 4,2 \leq y \leq 3 x$$

Answer

$=568$

You must be logged in to bookmark a video.

...and 800,000 more!

## Discussion

## Video Transcript

Okay, so we have this double Integral. Two, two, four, and then two to three effects. James. Trade three eggs, actually. Okay. And then to x six y deride X start with an anti derivative with respect. Why? So it's going to give us Teo X Y plus three. I squared. Okay. And we need to evaluate this. Who from, like ALS to try elsewhere? No. Michael's two to three eggs, brother. Okay, so two to four. This is gonna be to X times. Okay, three X minus two, and then plus three times nine x squared. Minus for Hey, so let's go ahead and distribute all this out. This is six X squared, minus four acts. What is THISS twenty seven X, uh, squared. My twelve. Okay. So anti derivative of this will be X go so divided by T to execute minus two x squared. And then that'LL be plus nine. Execute minors. Talk Max. Evaluated from two to four. This will be to times for cubed minus two cubes of sixty four minus eight. Okay, that is two times sixteen minus full. Kirk plus nine times sixty form and say minus twelve times. Uh, four minus two Okay, Two times. Fifty six. That's one twelve Minus two times twelve. Twenty four, nine times fifty six. Okay, ten times fifty six is five. Sixty and announce. Attract one fifty six. So that'LL be what? Five. Oh, for and then minus another twenty four. Okay, so one twelve and five o four. That's six sixteen. And then minus forty eight. Yeah, that should be five sixty eight.