(Solved): Change the Cartesian integral \( \int_{0}^{2} \int_{0}^{y} x d x \) dy into an equivalent polar in ...

Change the Cartesian integral \( \int_{0}^{2} \int_{0}^{y} x d x \) dy into an equivalent polar integral. Then evaluate the polar integral. Choose the correct equivalent polar integral below. A. \( \int_{0}^{2 / \sin \theta} \int_{\pi / 4}^{\pi / 2} r^{2} \cos \theta d r d \theta \) B. \( \int_{\pi / 4}^{\pi / 2} \int_{0}^{2 / \sin \theta} r^{2} \cos \theta d r d \theta \) C. \( \int_{0}^{2 / \sin \theta} \int_{0}^{\pi / 2} r^{2} \cos \theta d r d \theta \) D. \( \int_{0}^{\pi / 2} \int_{0}^{2 / \sin \theta} r^{2} \cos \theta d r d \theta \) The value of the double integral is (Type a simplified fraction.)