数学试题讲解

累次积分

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

等于

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

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

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

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