清华大学：《微积分》课程教学资源_复习 2：平行截面面积为已知的立体体积

6.二重积分计算的种积分顺序r=/(x,)drdy D:x1()≤x≤x2() csy≤d x10y) x2() D f∫(x,y)dx x1(y) 囧

0 y x c d y D x1 (y) x2(y) I = 6. 二重积分计算的两种积分顺序 .  = D I f (x, y)dxdy    ( ) ( ) ( )d x y x y f x, y x D: x1 (y)  x  x2 (y) c  y  d

6.二重积分计算的两种积分顺序r=∫/(x,p)dy D:x1()≤x≤x2() D:y1(x)≤y≤y2(x) ≤y≤d a≤x<b y2(x) x10y) x2() D D y1(x) x b x2(y) J2 f(x, y)dx f(x, y)dy x1(y) 囧

0 y x c d y  d c dy D D: y1 (x)  y  y2 (x) a  x  b 0 y x I = a b y1 (x) y2(x) D x1 (y) x2(y) x    ( ) ( ) ( , )d y x y x I = f x y y 6. 二重积分计算的两种积分顺序 .  = D I f (x, y)dxdy    ( ) ( ) ( )d x y x y f x, y x D: x1 (y)  x  x2 (y) c  y  d

6.二重积分计算的两种积分顺序r=∫/(x,p)dy D:x1()≤x≤x2() D:y1(x)≤y≤y2(x) ≤y≤d a≤x<b y2(x) x10) x2() D D y1(x) x b x2(y) J2 f(x, y)dx f(x, y)dy 囧

0 y x c d y D 0 y x I = a b y1 (x) y2(x) D x1 (y) x2(y) x 6. 二重积分计算的两种积分顺序 .  = D I f (x, y)dxdy    ( ) ( ) ( , )d y x y x I = f x y y    ( ) ( ) ( )d x y x y f x, y x  d c dy D: x1 (y)  x  x2 (y) c  y  d D: y1 (x)  y  y2 (x) a  x  b

6.二重积分计算的两种积分顺序r=∫/(x,p)dy D:x1()≤x≤x2() D:y1(x)≤y≤y2(x) ≤y≤d a≤x<b y2(x) x10) x2() D D y1(x) x b x2(y) b J2 f(x, y)dx f(x, y)dy 囧

0 y x c d y D 0 y x I = a b y1 (x) y2(x) D x1 (y) x2(y) x  b a dx 6. 二重积分计算的两种积分顺序 .  = D I f (x, y)dxdy    ( ) ( ) ( , )d y x y x I = f x y y    ( ) ( ) ( )d x y x y f x, y x  d c dy D: x1 (y)  x  x2 (y) c  y  d D: y1 (x)  y  y2 (x) a  x  b

7.计算 = J d tpe dxdj D:y≤x≤y21≤y≤ dy r ty 3兀 122l2 x=y 3 囧

0 y x 1 1 3 3 y = x x = y D 2     + = y y x x y y I d    dy .       + =     x y D y x y y x y y I D d d : . ln 2 2 1 12 3 = −  . 7. 计算