20

d

cos 0

f(rcos ,rsin )rdr (

10

).(B)(D)

10

(1)

R2

e

y2

dy

2x 1

y0

e

x2

dx y2

dy

R2 y20

e

xdx;

2

(A)(C)

dy

010

y y2

f(x,y)dx;dy

1 y20x 00x2

f(x,y)dx;f(x,y)dy.

1 x2(2)I

21

31

dx

eydy; x

dy 2y

42

2

10

dyf(x,y)

dy;

10

dy

(3)

).

dxsindsin

x xdy.2y

u07B设f(x,y)是连续函数,则二次积分dxf(x,y)dy (

x 1

x 1

(A)1dyy 1f(x,y)dx 22y)dx;

0 11

dy

y 1 1

f(x,(B)1y 10dy 1f(x,y)dx;(C)12y2 1

0dyy 1 1f(x,y)dx

1

dy

1

f(x,y)dx;

(D)

2y2 1

dy

1

f(x,y)dx.

07C交换下列二次积分的次序:(1)41

dy2(y 4)f(x,y)dx.

0 4 y

(2)1dy2yf(x,y)dx 3dy3 yf(x,y)dx.

001

(3)1d

(x,y)dy.0

(4)

2d

asin2 f(r, )dr.0

(5)I

0 2

df(x,y)dy

2 x2dx

40

2 xf(x,y)dy

2

(6)1dy1 y2f(x,y)dx.

1 y

(7)

1dx

4 x2f(x,y)dy

3

dx

4 x2

f(x,y)dy.

1 1 x2

11

07D计算下列累次积分:07E设f(x,y)在D上连续,证明:duf(t)dt

(x u)f(u)du.

00

07Fady

yem(a x)f(x)dx a证明

(a x)em(a x)f(x)dx.

08A由曲线x2 y2 2x,x2 y2 4x,y x,y 0所围成的图形的面积

S ().(A)

1

4

(2 );(B)

1

2(2 );(C)34

(2 );

(D)2 .

08B计算下列二重积分:(1)I

xdxdy

,其中D {(x,y)|y2 2x,0 x 2};

D

x2 y2

(2)I

(1 x)1 cos2ydxdy,其中D是y x 3,y

x 5

, D

22y 2

,y

2围成.(3)I

ydxdy,其中D是由曲线

b

1及x轴,y轴所围成的闭区D

域.

08C计算下列二重积分:(1)

yd ,其中D是由曲线r 2(1 cos )的上半部分与极轴所围成的区域;

D

(2)

x2 y2dxdy,其中D由y x与y x4围成;D

(3)

R2 x2 y2dxdy,其中D:x2 y2 Rx;

D