Double Integral Problem.

• Feb 17th 2010, 11:49 AM
Penguin91
Double Integral Problem.
I'm trying to calculate the following problem, however, when I take the integral of G with respect to y, my limits tend towards infinity. I can only think of using polar co-ordinates to solve this, but I'm not sure how it would apply in a case where one of the limits is 3-7y...

Let G be the region described by the inequalities 0 ≤ x ≤ 3 − 7y
and 0 ≤ y. Present a sketch of the region G and calculate the
double integral of the function f (x, y) = 2x + y^2 over G.
• Feb 17th 2010, 11:55 AM
icemanfan
This integral should work:

$\displaystyle \int _0 ^3 \int _0 ^{3-7y} (2x + y^2) dx \cdot dy$
• Feb 17th 2010, 12:01 PM
Penguin91
Thanks, how did you get the three? I'm assuming you substituted y=0 in the limit 3-7y
• Feb 17th 2010, 12:15 PM
icemanfan
Quote:

Originally Posted by Penguin91
Thanks, how did you get the three? I'm assuming you substituted y=0 in the limit 3-7y

Sorry, I made a mistake. The correct integral should be

$\displaystyle \int _0 ^{3/7} \int _0 ^{3-7y} (2x + y^2) dx \cdot dy$

Solve $\displaystyle x = 3-7y$ for y and you get the correct result.