calculo iii-lista 1

Professor Anatoli CLCULO III Lista 1 05.11.98 EXERCCIOS

Pgina 1 de 1

Troque a ordem de integrao:

1. 1

0

3

2

x

x

dydx)y,x(f

2. 1

0

3

21

2

2

y

y

dxdy)y,x(f

3. 1

0

2 2x

x

dydx)y,x(f

4. 1

0

2

3

x

x

dydx)y,x(f

5. 2

0

2x

x

dydx)y,x(f

6.

1

0

x

x

e

e

dydx)y,x(f

7.

a ax

xax

dydx)y,x(f2

0

2

2 2

8. 1

0

2 y

y

dxdy)y,x(f

9. 1

0

23 y

y

dxdy)y,x(f

10.

1

0

3

1

2

2

y

y

dxdy)y,x(f

Calcule a rea da regio limitada pelas curvas: 1. yx,xy 95253 22 == 2. 222 =+= x,xy 3. 02 === y,xcosy,xcosy 4. xxy,xxy 524 22 == 5. 0424 2 =+= yx,yx 6. 310 xy,x,y === 7. xey,x,y,x ==== 200

8. x

y,y,y,x 1310 ====

9. yyx,xy,y 21 22 =+== 10. 222 =+= x,xy

Calcule o volume limitado pelas superfcies:

1. 40

00822

=++=

===+

zyx,z,y;x,yx

2. 00422 2 ===++= z,y,zyx,yx 3. 014 22 ==++ z,zyx 4. 01222 ===+= z,y,xy,yxz

5. 000

424 2

===

=+=

z,y,x,yx,xz

6. 040

102

===

===

z,y,y,x,x,xyz

7. 095 22 ==+= z,yx,yz

8. 0063

12236===+

=+=++

z,y,yx,yx;zyx

9. 001

1 2

===

=++=

z,y,x,xy,yxz

10. 40 22 =+== yx,xyz,z

11. 0222

2222

===

=++=

z,xyx

,xyx,yxz


Pgina 2 de 2

Calcule as integrais duplas:

1. 20 pipi

+ yo,x:dycose ysenx

2. ( ) 21022 ====+

y,y,x,xy:dyx

3. ( ) 2023 22 ===+

y,yx,x:dyxyx

4. ( ) 212 ===+

x,xy,xy:dysenxcos

5. ( )

++=+

33293 22 xy,yxdyx

6. ( ) xy,y,x:dyxsen ===+ 2

0 pi

7. ( ) ( ) ( )542732 ,C,,B,,A:dx BC

A

8. ( ) 201022 ====+

y,y,x,x:dyy

9. 100 =+==

yx,y,x:dxy

10. ( ) 3002 =+==+

yx,y,x:dyx

11. 202 =+==

yx,y,xy:dy

12. x

y,xy,x:dyx 1222 ===

13. ylnx,y,y,x:dxdyex

====

210

14. ( ) ty,xy,x:dyxcos ===+

0

15. ( ) 156 ===+

x,xy,xy:dyx


Pgina 3 de 3

Calcule as integrais duplas usando a mudana de variveis:

1. 11 22

2

2

2

2

2

2

=+ b

ya

x:d

by

a

x

2. baqpbyx,ayx,qxy,pxy:

d


Pgina 4 de 4

LISTA DAS RESPOSTASOrdem de integrao

1. +3

2

1

31

2

0

21

31 y

y

y

dxdy)y,x(fdxdy)y,x(f

2.

+

+

3

2

3

0

2

21

1

0

21

0

2

0

2x

x

dydx)y,x(f

dydx)y,x(fdydx)y,x(f

3.

+2

1

2

0

1

0 0

2yy


4. 1

0

3 y

y

dxdy)y,x(f

5. +4

2

2

2

2

02

y

y

y


6. +e

ylne y

ln

dxdy)y,x(fdxdy)y,x(f1

11

1

1

1

7. ++

+a a

yaa

a yaa

a

y

dydx)y,x(fdxdy)y,x(f0

2

02

22

22

2

8.

+2

1

2

0

1

0 0

xx


9.

+3

1

23

0

1

0 0

2x

x


10.

+1

0

1

0

0

1

1

0

2 xx


rea da regio 1. 5 2.

332

3. 21

4. 2

27 5.

34

6. 41

7. 12 e 8. 3ln

9. 42

1 pi+

10. Correo: ( ) 414 222 =+= yx,xy

Resposta: 82 pi Volume do corpo

1. 3

2328 pi 2. 217

3. 4pi

4. 10588

5. 3

40

6. 9

32 7. 90 8. 12

9. 6079

10. 4 11. 3245pi

Integrais duplas 1. ( )( )11 piee 2. 5 3.

21244

4. Correo: pi=+== yx,y,x: 4400

Resp.: ( )22141 +pi 5.

169432

6. 1 7. 26

8. 3

14 9.

241

10. 2

27

11. 65

12. 49

13. 21

14. 2 15. 3125

Mudana de variveis 1. abpi32 2. ( )( )abpq 31 3. 320 4. 1 5. 24 6. 43 7. 6 8. pi54 9. ( ) 392 43 Rpi 10. pi32

calculo iii-lista 1

Documents