Help with Change of Variable in Multiple Integral Question

An ellipse is given by

$\frac{x^2}{a} +\frac{y^2}{b} = 1$

You want to find the area by using a change of coordinates:
x = r cos θ, y =$\frac{br}{a}$sin θ.
Find the range of values of r and θ that correspond to the interior of the ellipse.

Find the Jacobian of the transformation.
Find the area.

Now the Jacobian I got was $J = \frac{br}{a}$

Now the problem is..... I don't know what to integrate...is it:

$\displaystyle\int^\pi_0\int^1_0 x^{2} + y^{2}\ dx dy$

then substituting in x = r cos θ, y =$\frac{br}{a}$sin θ

$\displaystyle\int^\pi_0 \int^1_0 [(rcos\theta)^{2} + (\frac{br}{a}sin^{2}\theta)]\frac{br}{a}drd\theta$

Because I haven't been given the function so I assumed it was integrating
$x^{2} + y^{2}$...Please check if my limits are right they are (2pi and 0) for the first integral....Don't know how to write 2pi in the integral using latex yet!

And if this is right....why can't I get the correct answer?

Thanks

post a photo of the question (saves you type too)

here it is

firstly apologies I refuse to use LaTeX

the area is the Integral of 1 dA, where dA is the area element

in other words dA = J dr dθ

the transformation they give you makes the ellipse into a circle of radius a

to sweep this area you need

r=0 to r=a

and

θ=0 to θ=2π

So is it?
A = $\displaystyle\int^{2\pi} _0 \int^1_0\frac{br}{a}drd\theta$

yup still getting used to $\mathrm{Latex!}$

I still don't understand how this question kind of transforms it into a circle

I was hoping you would not ask ....

well

first multiply the ellipse as given by a²

x² + (a²y²)/b²

then X = x, Y =( ay/b )

X² + Y² = a²

wow that is some trick of playing around I will have to learn haha

Thanks