数学试题讲解

设

D = {(x, y) ∣ x^{2} + y^{2} \leq 2 x, x^{2} + y^{2} \leq 2 y}

，函数

f (x, y)

在

D

上连续，则

\iint_{D} f (x, y) d x d y = ()

\int_{0}^{\frac{π}{4}} d θ \int_{0}^{2 \cos θ} f (r \cos θ, r \sin θ) r d r + \int_{\frac{π}{4}}^{\frac{π}{2}} d θ \int_{0}^{2 \sin θ} f (r \cos θ, r \sin θ) r d r

\int_{0}^{\frac{π}{4}} d θ \int_{0}^{2 \sin θ} f (r \cos θ, r \sin θ) r d r \int_{\frac{π}{4}}^{\frac{π}{2}} d θ \int_{0}^{2 \cos θ} f (r \cos θ, r \sin θ) r d r

\int_{\frac{π}{4}}^{\frac{π}{2}} d θ \int_{0}^{2 \cos θ} f (r \cos θ, r \sin θ) r d r

2 \int_{0}^{1} d x \int_{1 - \sqrt{1 - x^{2}}}^{x} f (x, y) d y