设函数f(x，y)连续，则∫12dx∫x2f(x,y)dy+∫12dy∫y4-yf(x,y)dx=( ).
A: ∫12dx∫14-xf(x,y)dy．
B: ∫12dx∫x4-xf(x,y)dy
C: ∫12dx∫14-yf(x,y)dy．
D: ∫12dx∫yyf(x,y)dy
A: ∫12dx∫14-xf(x,y)dy．
B: ∫12dx∫x4-xf(x,y)dy
C: ∫12dx∫14-yf(x,y)dy．
D: ∫12dx∫yyf(x,y)dy
举一反三
- 设函数f（x，y）连续，则∫12dx∫x2f（x，y）dy+∫12dx∫y4—yf（x，y）dy=（ ） A: ∫12dx∫14—xf（x，y）dy B: ∫12dx∫x4—xf（x，y）dy C: ∫12dx∫14—xf（x，y）dy D: ∫12dx∫y2f（x，y）dy
- 累次积分∫01dx∫x1f（x，y）dy+∫12dy∫02—yf（x，y）dx可写成（ ） A: ∫02dx∫x2f（x，y）dy B: ∫01dx∫x2—yf（x，y）dy C: ∫01dx∫x2—xf（x，y）dy D: ∫01dx∫y2—yf（x，y）dy
- 形如（ ）的方程，称为可分离变量方程，这里\(f(x), g(y)\)分别为\(x, y\)的连续函数。 A: \(\frac{dy}{dx}=f(x)g(y)\) B: \(\frac{dy}{dx}=f(x)\) C: \(\frac{dy}{dx}=f(x)+g(y)\) D: \(\frac{dy}{dx}=\frac{f(x)}{g(y)}\)
- 函数\(z = {x^y}\)的全微分为 A: \(dz = y{x^{y - 1}}dy + {x^y}\ln xdx\) B: \(dz = y{x^{y - 1}}dx + {x^y}dy\) C: \(dz = y{x^{y - 1}}dx + {x^y}\ln xdy\) D: \(dz = y{x^{y - 1}}dy + {x^y}dx\)
- 交换积分次序∫21dy∫2yf（x，y）dx=∫21dx∫x1f(x，y)dy∫21dx∫x1f(x，y)dy．