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CHAPITRE 5. CALCULS D'INTÉGRALES DOUBLES, TRIPLES ET DE SURFACE
Exercice 5.6. 1 - {[
dx dy
·
- Jiv (I + x 2 )(1 + y 2 ) '
'D = { (x, y) E JR. 2 1 Ü:::;; X:::;; 1 ; Ü:::;; y:::;; X}·
Exercice5.7. 1= JfvaxbYdxdy ;'D={(x,y)E!R. 2 lx~O; y~O; x+y::;;;
1 }·
Exercice 5.8. fo
3
(~ 1
e-Y
2 dy) dx.
Exercice 5.9. 1 = {[ sin 7rX dx dy;
}}D
2y
D = { (x, y) E IR. 2 l I:::;; x:::;; 4 ; yx:::;; y:::;; min{2, x} }.
.
/J~
dx dy
Exercice 5.10. 1 =
J 2 2
2
2 2 ;
V
X +y (I +X +y )
'D = { (x, y) E JR.2 1 x2 + y2 :::;; a2 }·
Exercice 5.11. 1 = ffv xyJ x 2 + 4y 2 dx dy;
D = { (x, y) E IR. 2 1 x ~ 0; y~ 0; x 2 + y 2 :::;; 1 }·
Exercice 5.12. 1 = {[ 2 dx dy 2 ; D = {Cx, y) E IR. 2 l 2:::;; x 2 + y 2 :::;; 4}.
j}DX +xy+y
Exercice5.13. 1= ffvxdxdy ;D={(x,y)EIR. 2 1x 2 +y 2 -2x:::;;O; x~I}.
Exercice 5.14. 1 = ffv y'XY dx dy ; D = { (x, y) E IR. 2 1 (x 2 + y 2 ) 2 :::;; xy}
Exercice 5.15. 1 = {[ 1 x;
2 dx dy ;
}}D +x +y
D = { (x, y) E IR. 2 10:::;; X :::;; 1 ; 0:::;; y:::;; 1 j x 2 + y 2 ~ 1}
Exercice 5.16. 1 = Jl (x 2 + y 2 ) dx dy;
D = { (x, y) E IR. 2 10:::;; y ; x 2 + y 2 - x:::;; 0; x 2 + y 2 - y~ 0}