Find the exact area of the surface
z = 1 + 2x + 3y + 4y2, 1 ≤ x ≤ 11, 0 ≤ y ≤ 1

Question

Find the exact area of the surface
z = 1 + 2x + 3y + 4y2, 1 ≤ x ≤ 11, 0 ≤ y ≤ 1

anonymous · Answer

I gave it a shot by trying to set up a double integral from 1 to 11 and from 0 to 1 and using the derivative in respect to x and y and plugging them directly into the formula

anonymous · Answer

I got a really complicated integral though so, knowing my homework, I doubt it's right.

ganeshie8 · Answer

SA = $\large   \iint \limits_D \sqrt{5 + (8y+3)^2 }dA$

anonymous · Answer

A = ∫∫ ( (∂z/∂x)^2 + (∂z/∂y)^2 + 1) dA

ganeshie8 · Answer

how did u set up the bounds ? maybe first do dx

anonymous · Answer

wow, I feel slightly dumb.  I didn't do the correct derivative with respect to y

ganeshie8 · Answer

haha happens... also choosing correct order greatly simplifies the work here

ganeshie8 · Answer

since the bounds are numerical, the answer wont depend on order of integration... you're free to switch the order

anonymous · Answer

okay, cool.  I'm sure I got it from here.  Thank you greatly!

ganeshie8 · Answer

np :)