Question

Determine the area of the part of the surface z=8+5x+1y2 that lies above the triangle with vertices (0,0) , (0,7) , and (13,7) .

Answer 1

So far I have double integral of sqrt(26+4y^2) dx dy x from 0 to 7/13y and y from 0 to 7

What am I doing wrong?

Answer 2

@ganeshie8 @sourwing

Answer 3

@mathmale

Answer 4

The surface area is on the surface z=8+5x+1y^2 above the triangular area in the xy plane whose vertices are given by (0,0), (0,7) and (13,7). Were we looking for the VOLUME of the solid underneath this surface, that'd be familiar to me, but finding the surface area of this curved surface is a new situation. Would you mind explaining how you have done this before? Have you examples in your textbook or online? A formula?

Answer 5

http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx

Answer 6

Are you positive that you're looking for surface area, and not for volume?

Answer 7

that link has a formula etc with a few examples. and yes the question says,

Determine the area of the part of the surface z=8+5x+1y2 that lies above the triangle with vertices (,00) , (0,7) , and (13,7) .


The surface area equals _________________________________

Answer 8

It's really cool that you've done your homework and have this ready reference regarding surface areas. I take it that you're familiar with partial derivatives. Right?

Answer 9

One circular table has a diameter of 9 ft, and another circular table has a diameter of 20 ft. How much greater is the area of the larger table? Round to the nearest whole number???

Answer 10

help please idk how to work this

Answer 11

yes and daniella why are you posting on my question?

Answer 12

idk how to work this

Answer 13

you post a question in the blank and wait for a response

Answer 14

Daniella: i'd be happy to help you, but only after I'm finished helping mgh20. Would you please post your own question, separately, not here in someone else's post. Thank you.

Answer 15

@mgb20: Familiar with partial derivatives?

Answer 16

yes mathmale i am

Answer 17

idk how to do that the blank not showing.. could i do it on my profile thing ?

Answer 18

daniella i can help. make a new question.

Answer 19

Here you have a function f(x,y) in two variables: f(x,y)=z= z=8+5x+y^2.

Please find the partial derivative of this with respect to x, and then with respect to y. In both cases you'll need to square the resulting derivative, according to Paul's notes.

Answer 20

david i have a diff question i posted 8 min ago

Answer 21

tag me there.

Answer 22

Fx=5, Fy=4y

Answer 23

\[f _{x}=?~~~~~f _{y}=?\]

Answer 24

sqrt(5^2 + (2y)^2 +1) = sqrt( 26+4y^2)

Answer 25

sorry Fy=2y

Answer 26

Nice work!

Now, according to Paul's Notes, we need to form the quantity\[\sqrt{((f _{x)^2}+(f _{y})^2}+1).\]Don't take my word for it; verify this with Paul's Notes. If you agree with this expression, substitute your \[f _{x}~and~f _{y}.\]

Answer 27

I did that above. I got \[\sqrt{26+4y^2}\]

Answer 28

I believe the 1 is still under the sqrt sign

Answer 29

that does indeed look correct. We are to integrate this expression over the triangular region defined by those 3 points, correct?

Answer 30

right.

Answer 31

yes

Answer 32

would you prefer to use horiz. strips or vertical strips?

Answer 33

Are you satisfied with the result you got via Wolfram? Have you found anything you did wrong initially but have done right this time?

Answer 34

We did everything exactly the same but its not the correct answer

Answer 35

I'm arbitrarily opting to use vertical strips. The top end of each strip will be y=7 and the bottom end of each will be y=(7/13)x. Can you agree with that?

Answer 36

\[\int\limits_{0}^{7} \int\limits_{0}^{7/13y}\sqrt{26+4y^2} dx dy\]

Answer 37

ohh shoot its the area ABOVE