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Problemas resueltosIntegración múltiple: integrales dobles
I SABEL M ARRERO
Departamento de Análisis Matemático
Universidad de La Laguna
imarrero@ull.es
Índice
1. Problema 1 1
2. Problema 2 2
3. Problema 3 3
4. Problema 4 4
5. Problema 5 6
6. Problema 6 7
7. Problema 7 8
8. Problema 8 9
9. Problema 9 10
10. Problema 10 11
11. Problema 11 12
12. Problema 12 13
13. Problema 13 14
14. Problema 14 15
15. Problema 15 16
,OCW-ULL 2011/12 C ÁLCULO I NTEGRAL V ECTORIAL
, I NTEGRACIÓN MÚLTIPLE : INTEGRALES DOBLES 1/17
1. Problema 1
Dibujar la región de integración y cambiar el orden en la integral
Z 1 Z |x|
dx f (x, y) dy.
−1 x2
Z √y
If this message does not
Z 1 Z −y Z 1
Solución: dy √ f (x, y) dx + dy f (x, y) dx.
0 − y 0 y
R ESOLUCIÓN . La región de integración se muestra en la Figura 1.
disappear after a short time, the
author either did not compile the
Figura 1.
√
Toda recta horizontal entre 0 y 1 entra en el dominio en un punto de abscisa x = − y y sale en un punto
LATEX file three times, or your √
de abscisa x = −y, para volver a entrar en un punto de abscisa x = y y salir en un punto de abscisa x = y. Por
tanto, la integral se reescribe en la forma
Z 1 Z −y Z 1 Z √y
dy √ f (x, y) dx + dy f (x, y) dx.
PDF viewer does not support 0 − y 0 y
OCG. Use Adobe Reader!
C ÁLCULO I NTEGRAL V ECTORIAL OCW-ULL 2011/12
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