Finding area of figures

First, we will covert the cartesian equation to polar coordinates, and solve for r: $r=\frac{1345(\cos \theta)^\frac{3}{2} (\sin \theta)^\frac{3}{2}}{(\cos \theta)^4+(\sin \theta)^4}$

Second, we will use the equation to find the area of a bounded region using polar coordinates which is $\int \frac{1}{2} r^2 d\theta$ , our lower limit would be 0 and our upper limit would be $\frac{\pi}{2}$

When we find the integral we will get $\frac{1345^2}{2} (\frac{-1}{4(1+(\tan \theta)^4)}).$ Now, when plugging in the lower and upper limits we will see that it is undefined, that is we will need to take $\lim_{\theta \to \frac{\pi}{2}} \frac{1345^2}{2} (\frac{-1}{4(1+(\tan \theta)^4)})$ and as $\lim_{\theta \to 0} \frac{1345^2}{2} (\frac{-1}{4(1+(\tan \theta)^4)}).$ When $\theta$ approaches $\frac{\pi}{2}$ the limit would be 0, and when $\theta$ aproaches 0 the limit would be 1.

Therefore, our solution would be $\frac{1345^2}{8}$ . Hence $1345 + 8 = 1353$