1
$\begingroup$

I'm trying to solve the following integral: $\iint\limits_D (10x^2+39xy+14y^2)^2 dxdy$ bounded by the lines: $2x+7y=1$, $2x+7y=-1$, $5x+2y=3$ and $5x+2y=-3$.

Now I'm new to calculus and do not know how to solve this kind of problem other than when say $x=a+by, x=c+by$, $y=0$ and $y=2$.

It doesn't look that advanced but I cannot find any similar examples. I'm expected to use Mathematica for the calculation.

Can I rotate the axes to simplify it? Or where do I start?

Thanks! Alexander

1 Answers 1

4

Hint: Take $u=2x+7y,v=5x+2y$ so you have the range of them as $u|_{-1}^{1}, v|_{-3}^3$ Now change the integrand according to $u$ and $v$ and calculate the Jacobian of them respect to $x$ and $y$ as well. See this link for more http://www.math24.net/change-of-variables-in-double-integrals.html

  • 0
    Nice smiley, and ++++answer!2013-02-27