数学试题讲解

设

D

是第一象限中曲线

2 x y = 1, 4 x y = 1

与直线

y = x, y = \sqrt{3} x

围成的平面区域, 函数

f (x, y)

在

D

上连续, 则

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

\int_{\frac{π}{4}}^{\frac{π}{3}} d θ \int_{\frac{1}{2 \sin^{2} θ}}^{\frac{1}{\sin^{2} θ}} f (r \cos θ, r \sin θ) r d r

. B.

\int_{\frac{π}{4}}^{\frac{π}{3}} d θ \int_{\frac{1}{\sqrt{2 \sin 2 θ}}}^{\frac{1}{\sqrt{\sin 2 θ}}} f (r \cos θ, r \sin θ) r d r

. C.

\int_{\frac{π}{4}}^{\frac{π}{3}} d θ \int_{\frac{1}{2 \sin 2 θ}}^{\frac{1}{\sin^{2} θ}} f (r \cos θ, r \sin θ) d r

. D.

\int_{\frac{π}{4}}^{\frac{π}{3}} d θ \int_{\frac{1}{\sqrt{2 \sin^{2} θ}}}^{\frac{1}{\sqrt{\sin^{2} θ}}} f (r \cos θ, r \sin θ) d r