Question

Just working on some practice problems. \(\int\int_R (4x+8y)dA\) where \(R\) is a parallelogram with vertices (-1,3),(1,-3) and (3,-1), (1,5); \(x=\frac{1}{4}(u+v)~,~ y=\frac{1}{4}(v-3u)\)

Answer 1

Hm..

Answer 2

you want to change parallelogram into a rectangle ?

Answer 3

Yeah, I guess.

Answer 4

I'm not sure where to begin exactly...can I get a hint? lol

Answer 5

Oh wait, do we even need to? We can just use these two equations to get the jacobian, right?

Answer 6

yeah looks you're given the transformation already

Answer 7

How do you write up matrices...

Answer 8

@ParthKohli transformations from cartesian to polar

Answer 9

```
\begin{vmatrix}
a&b\\
c&d
\end{vmatrix}
```
produces

\[\begin{vmatrix}
a&b\\
c&d
\end{vmatrix}\]

Answer 10

\[\left|\frac{\partial(x,y)}{\partial(u,v)}\right|=\left[\begin{matrix}\frac{1}{4} & \frac{1}{4} \\ \frac{1}{4} & \frac{1}{4}\end{matrix}\right] \]

Answer 11

Why am I not getting this..