Multiple Integral over Polar Coordinate

Formula for the double integral in polar coordinates is

Which of the following is the polar coordinate for the Cartesian coordinate (x,y) = (1,1) ?

•  $\left(1,\frac{\pi}{4}\right)$  

•  $\left(\sqrt{2},\frac{\pi}{4}\right)$  

•  $\left(1,\frac{3\pi}{4}\right)$  

•  $\left(\sqrt{2},\ \frac{3\pi}{4}\right)$  

When the double integral

 $\int_{ }^{ }\int_R^{ }\ \ f\left(x,y\right)dA$  is in its polar form, which of the following is the correct double integral?

•  $\int\int_R^{ }\ \ f\left(x,y\right)\ drd\theta$  

•  $\int_{ }^{ }\int_R^{ }\ f\left(r,\theta\right)\ drd\theta$  

•  $\int_{ }^{ }\int_R^{ }\ f\left(x,y\right)\ rdrd\theta$  

•  $\int_{ }^{ }\int_R^{ }\ f\left(r,\theta\right)\ rdrd\theta$  

Find the area of the given region. Give your answer correct to 2 decimal places.