cours 21
3.4 INTÉGRALE
TRIPLE
Au dernier cours, nous avons vu
Applications de l’intégrale double.
L’aire d’une surface.
Aujourd’hui, nous allons voir
Intégrale triple Type I, II et III Volumes
Applications
On sait déjà qu’il est difficile de visualiser les fonctions à plus de deux variables.
w
<latexit sha1_base64="BmTmZClXpLIB2bw14MWSaeMELpA=">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</latexit>= f (x, y, z )
Car son graphe est un sous-ensemble de . R
<latexit sha1_base64="srBKwsXQ2HvP5UMdYEmRKcEubqE=">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</latexit> 4Malgré ça, les idées développées pour l’intégrale double se
généralisent très bien.
n,m,l
lim
!1X
ni=1
X
mj=1
X
lk=1
f (x
i, y
j, z
k) V =
ZZZ
B
f (x, y, z )dV
<latexit sha1_base64="hueyAuUSxGkZ4lUwdTqsN9cBzEA=">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</latexit>
=
Z
sr
Z
dc
Z
ba
f (x, y, z )dxdydz
<latexit sha1_base64="wz+JAXh/2ioVmJWZjNSaoB82TWk=">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</latexit>
(Fubini)
Exemple
Z
32
Z
20
Z
21
x
2yz dxdydz
<latexit sha1_base64="/KCFMB19Y6Ic5c0wlWH5RSNNJw8=">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</latexit>
=
Z
32
Z
20
x
3yz 3
2
1
dydz
<latexit sha1_base64="+37SIErM+yubxxxVlCE23PnWUpk=">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</latexit>
= 7 3
Z
32
Z
20
yzdydz
<latexit sha1_base64="QhwJaBym50zDJAp/fB0DB2rl03k=">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</latexit>
= 7 3
Z
32
y
2z 2
2
0
dz
<latexit sha1_base64="CcRTGlIQvvlHBihbeDGyd2+dC/s=">AAADUHicjVLLbtNAFD1xWigpjxSWbCwipK4i20EqG6SqbFgWqWkrNU1kTyZhVMe2xuNKqfFf8DVs4QvY9Q/KH7Ard26mErTiMZbtM+eec2funUmKVJUmCC5bXntt/d79jQedzYePHj/pbj09LPNKCzkUeZrr4yQuZaoyOTTKpPK40DJeJKk8Ss7e2vjRudSlyrMDsyzk6SKeZ2qmRGyImnT7b0YzHYt6p6kHzUhlZhKNBytqOY4umjpqRntq/nESjCN/ejHp9oJ+wMO/C0IHenBjP99qrWOEKXIIVFhAIoMhnCJGSc8JQgQoiDtFTZwmpDgu0aBD3opUkhQxsWf0ndPsxLEZzW3Okt2CVknp1eT08ZI8Oek0Ybuaz/GKM1v2T7lrzmn3tqR/4nItiDX4QOy/fDfK//XZWgxmeM01KKqpYMZWJ1yWirtid+7/UpWhDAVxFk8prgkLdt702WdPybXb3sYcv2KlZe1cOG2F73+tzjrO3Qp2V1YpmdHcqVWdNZ+2Im3BXV8SMvTl86TbE96+K3fBYdQPB/3w/ave7p67Rxt4jhfYpruyg128wz6GtI9P+Iwv+Op983541+3WSuq5P57ht9Hu/AQG6LPH</latexit>
= 14 3
Z
32
zdz
<latexit sha1_base64="ZmGX02yWfyZApit2u56mQrmQpIA=">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</latexit>
= 14 3
✓ 9 2
4 2
◆
<latexit sha1_base64="0PzgrBorf3QRdFYJM4eyi8MpNi4=">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</latexit>
= 35 3
<latexit sha1_base64="BP/eBOxtYtYmzvE6JZyBJMxZk+I=">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</latexit>
=
Z
32
Z
20
(2
31
3)yz
3 dydz
<latexit sha1_base64="kZ2Iqi56eOTJhlWp4/Vh9Be98N0=">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</latexit>
= 7 3
Z
32
(2
20
2)z
2 dz
<latexit sha1_base64="D2pTsJEATJNTgISnXv93WKcKMpg=">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</latexit>
0 car fonction impaire.
3 fois le volume de la sphère
Exemple ZZZ
x2+y2+z2R
3 + x
3+ 4 sin z dV
<latexit sha1_base64="QekqMzSTuhn/UIxIJI9F1m6SZqQ=">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</latexit>
=
ZZZ
x2+y2+z2R
3 dV +
ZZZ
x2+y2+z2R
x
3dV +
ZZZ
x2+y2+z2R
4 sin z dV
<latexit sha1_base64="MPjw5JZBrTDUJEAYVw0RriD1yPU=">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</latexit>
= 4⇡
<latexit sha1_base64="s4PV1I2U262MV1tbYyp9F3qaeb8=">AAADKXicjVLJTtxAFKwxkBDIwnLMxWIUKaeRHZCSSyQULhwBZVgEJLJNQ1p4U7uNNBrxFVzhC/gabpBrLuQvqH40EouytGW7ul7V636vO61z3dgouuoEI6Njz56Pv5iYfPnq9Zup6Zn1pmpNpvpZlVdmM00aletS9a22udqsjUqKNFcb6eGSi28cKdPoqvxqB7XaLZKDUu/rLLGktj4v7NQ6XPs2/32qG/UiGeFTEHvQhR8r1XRnDDvYQ4UMLQoolLDEORI0fLYRI0JNbhdDcoZIS1zhGBP0tlQpKhKyh/wecLbt2ZJzl7MRd8ZVcr6GzhDv6KmoM8RutVDirWR27J9yDyWn29uA/9TnKsha/CD7L9+d8n99rhaLfXySGjRrqoVx1WU+SytdcTsP71VlmaEm5/Ae44Y4E+ddn0PxNFK7620i8WtROtbNM69t8fuv1TnHkV/B7coplTBGOnVb51BOW1NbS9cHRJZfOU/envjxXXkK1j/04vlevLrQXfzi79E43mIO73lXPmIRy1hBn/socIJTnAXnwUVwGfy8lQYd75nFgxH8ugFHZKXP</latexit>R
3Faites les exercices suivants
p. 880 # 1 et 2
p. 880 # 1 et 2
a
<latexit sha1_base64="KlSGEXQz4iKFrU+Hg9x+KbTHwjw=">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</latexit> x b
f
<latexit sha1_base64="uvKZu3tUHJNBHfYrjKYhB2+wQu8=">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</latexit> 1(x) y f
2(x) g
<latexit sha1_base64="Pi7gpo/nt3bx7Af4ww73gqrY+R8=">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</latexit> 1(x, y ) z g
2(x, y )
Type I
a
<latexit sha1_base64="KlSGEXQz4iKFrU+Hg9x+KbTHwjw=">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</latexit> x b
f
1(x) y f
2(x)
<latexit sha1_base64="uvKZu3tUHJNBHfYrjKYhB2+wQu8=">AAADDnicjVI9T9xAEH044ZuQIxQUNFZOSNCcbIIEJSJNSiLlAAnQyTZ7ZIXPNvYaYZ3yH/IfaENLF9HmL+QfJB0/gbfDEiVBCNby+u2beeOZ2YmLVFcmCH6OeC9ejo6NT0xOTc+8mn3dmnuzU+V1mahukqd5uRdHlUp1prpGm1TtFaWKBnGqduOT99a+e6bKSufZJ9MU6nAQHWe6r5PIkOq1Fvq9cPl85SBVp34je7+3SqLXagedQJb/EIQOtOHWdt66wQGOkCNBjQEUMhjiFBEqPvsIEaAgd4ghuZJIi13hC6aoreml6BGRPeF+zNO+YzOebcxK1An/kvItqfSxRE1Ov5LY/s0Xey2RLftY7KHEtLk1/MYu1oCswWeyT+nuPZ+rs7UY9LEhNWjWVAhjq0tclFq6YjP3/6rKMEJBzuIj2kviRJT3ffZFU0nttreR2H+Jp2XtOXG+NX67LBXOJGrzJ/uh3KGmvZBeNkSGu9wSRyL8fwAegp3VTviuE35ca29uueGYwCLeYpkTsI5NfMA2ulLxBb7h0vvqXXnfves7V2/Eaebxz/J+3AIM7aNI</latexit>
g
<latexit sha1_base64="Pi7gpo/nt3bx7Af4ww73gqrY+R8=">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</latexit> 1(x, y ) z g
2(x, y) Type I
c
<latexit sha1_base64="OIjcidnsYy9HU3PdLcU0jpODZC4=">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</latexit> y d
f
1(y ) x f
2(y )
<latexit sha1_base64="VKRXxE1WJMuIqrPzM5iKHs7PkI8=">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</latexit>
g
<latexit sha1_base64="Pi7gpo/nt3bx7Af4ww73gqrY+R8=">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</latexit> 1(x, y ) z g
2(x, y )
Type II
g
<latexit sha1_base64="ddVGgC83acSAIkMND7aB3eVbCTs=">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</latexit> 1(y, z ) x g
2(y, z )
Type III
g
1(x, z ) y g
2(x, z )
<latexit sha1_base64="1sLiAu3bA92aZtbT00VfJzH9k0Q=">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</latexit>
Exemple Z
10
Z
x2 xZ
x y 1xy + z dzdydx
<latexit sha1_base64="Gp5x3KjWccgckxV0StO24WtybA8=">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</latexit>
=
Z
10
Z
x2x
xyz + z
22
x y
1
dydx
<latexit sha1_base64="9pcnrgFN649HTMDIjsSygLxwFjM=">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</latexit>
=
Z
10
Z
x2x
xy (x y ) + (x y )
22 + xy 1
2 dydx
<latexit sha1_base64="Kjj07p18uR4fgs36POxKIlKnulM=">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</latexit>
=
Z
10
Z
x2x
x
2y xy
2+ x
22xy + y
22 + xy 1
2 dydx
<latexit sha1_base64="bp4McCmZB6+UL132IpzEuH2zRcg=">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</latexit>
=
Z
10
Z
x2 xx
2y xy
2+ x
2+ y
22
1
2 dydx
<latexit sha1_base64="MkD+vOwT/PxdDj3VfDV2em+REpk=">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</latexit>
=
Z
10
x
2y
22
xy
33 + x
2y
2 + y
36
y 2
x2 x
dx
<latexit sha1_base64="vBoxcIVmgNAzmsrYPK6nIYUjqxU=">AAADkHicjVJRT9RAEJ5SQASBAx99abyYkBgu7Z1RXoyoL8YnTDggofTS7u0dG3pts92Sa2r/pS/+A/0LPjkz7EWFKG7T9ttvvm92Z3aTIlWl8f2vzpK7vLL6YO3h+sajza3tzs7uSZlXWsihyNNcnyVxKVOVyaFRJpVnhZbxLEnlaXL1nuKn11KXKs+OTV3Ii1k8zdREidggNepkr0OVmZEfBWEqJ6bnhRMdi2Ye9euo3zb9dt8SdTRom0H7/FeconbKwZcLLUdCraaX5vOo2Z+3Eenb0BvPR52u3/N5eHdBYEEX7DjKd5wVCGEMOQioYAYSMjCIU4ihxOccAvChQO4CGuQ0IsVxCS2so7dClURFjOwVfqc4O7dshnPKWbJb4CopvhqdHjxDT446jZhW8zhecWZi/5a74Zy0txr/ic01Q9bAJbL3+RbK//VRLQYmcMA1KKypYIaqEzZLxV2hnXu/VWUwQ4Ec4THGNWLBzkWfPfaUXDv1Nub4N1YSS3NhtRV8/2d15Li2K9CuSCmZ0dypmzobPm2F2oK7XiMy+OXzxNsT3L4rd8FJvxcMesGnF93Dd/YercETeAp7eFdewSF8gCMY4j6+wA/HdZbdXffAfeO+vZEuOdbzGP4Y7sefIy3KHQ==</latexit>
Exemple Z
10
Z
x2 xZ
x y 1xy + z dzdydx
<latexit sha1_base64="Gp5x3KjWccgckxV0StO24WtybA8=">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</latexit>
=
Z
10
x
2y
22
xy
33 + x
2y
2 + y
36
y 2
x2 x
dx
<latexit sha1_base64="vBoxcIVmgNAzmsrYPK6nIYUjqxU=">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</latexit>
=
Z
10
x
2y
22 + y
3(1 2x)
6 + y (x
21) 2
x2 x
dx
<latexit sha1_base64="8ZzrPisMObqaU78iikQAzbLfWQg=">AAADf3icjVLbbtNAEJ3UFEq5NIVHXiwiRCoUy3YRlwekCl54LBJpK9VxZG826aqOba3XVSzjr+Mr+AN4hR9gZrJFQMVlo9hnz5wzOzPetMxUZXz/U2/DubZ5/cbWze1bt+/c3env3juqiloLORZFVuiTNKlkpnI5Nspk8qTUMlmmmTxOz99Q/PhC6koV+XvTlHKyTBa5miuRGKSm/cmrSOVm6sdBlMm58dxorhPRruKwicOuDbsna6KJ94fBKFztde2zH9wQZaNgj2SRVosz82HajlZdTPYucmeraX/gez4v9yoILBiAXYfFbm8TIphBAQJqWIKEHAziDBKo8HcKAfhQIjeBFjmNSHFcQgfb6K1RJVGRIHuOzwXuTi2b455yVuwWeEqGf41OFx6hp0CdRkynuRyvOTOxf8rdck6qrcF3anMtkTVwhuy/fJfK//VRLwbm8IJ7UNhTyQx1J2yWmqdClbs/dWUwQ4kc4RnGNWLBzss5u+ypuHeabcLxz6wklvbCamv48tfuyHFhT6CqSCmZ0TypdZ8tf22F2pKn3iAy+OTvibcn+P2uXAVHoRfse8G7p4OD1/YebcEDeAhDvCvP4QDewiGMsY6PWPFX+Ob0nMeO5/hr6UbPeu7DL8t5+R3A9sLv</latexit>
=
Z
10
✓ x
42 + x
6(1 2x)
6 + x
2(x
21) 2
◆ ✓ x
32
x
3(1 2x) 6
x(x
21) 2
◆
dx
<latexit sha1_base64="juRMHWZChZ8FeZCfxSn68QkL9dc=">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</latexit>
=
Z
10
x
42 + x
66
x
73 + x
42
x
22
x
32 + x
36
x
43 + x
32
x
2 dx
<latexit sha1_base64="fvR2gTvgkdR+OM4a4qg6sPBCkSs=">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</latexit>
=
Z
10
2x
43 + x
66
x
73
x
22 + x
36
x
2 dx
<latexit sha1_base64="vNMFcurZqYb3C6e4yn/6m1E212Q=">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</latexit>
Exemple Z
10
Z
x2 xZ
x y 1xy + z dzdydx
<latexit sha1_base64="Gp5x3KjWccgckxV0StO24WtybA8=">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</latexit>
=
Z
10
2x
43 + x
66
x
73
x
22 + x
36
x
2 dx
<latexit sha1_base64="vNMFcurZqYb3C6e4yn/6m1E212Q=">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</latexit>
= 2x
515 + x
742
x
824
x
36 + x
424
x
24
1
0
<latexit sha1_base64="WIYAqKQ/fMh8Ykqi73NIvDRzh/U=">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</latexit>
= 2
15 + 1 42
1 24
1
6 + 1 24
1 4
<latexit sha1_base64="UKXENVegMtbM/6O6UnN0FK/Lqe0=">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</latexit>
= 2
15 + 1 42
7 42
1 4
<latexit sha1_base64="ulYa6qqsxcVwQPTQfjp1+Ok3SkI=">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</latexit>
= 8 60
6 42
15 60
<latexit sha1_base64="atAqVmOmDrsIag5n8VhOEuuO8ro=">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</latexit>
= 1 7
7 60
<latexit sha1_base64="BZI+MseBF8ZSpC4HIYlHvRaAsSY=">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</latexit>
= 60 420
49 420
<latexit sha1_base64="s1L8ONQ3KFW26FwtytK6Ms4kIjM=">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</latexit>
= 109 420
<latexit sha1_base64="3PNUah7t2+sZ4O1Q0Dj60e81Who=">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</latexit>
Faites les exercices suivants
p.880 # 3 à 8
p.880 # 3 à 6
Exemple ZZZ
E
xy dV
<latexit sha1_base64="HVvOym2w+/55USwXPrgSADrLLlg=">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</latexit>
(0, 0, 0)
<latexit sha1_base64="lEJbA+jiIF1G8/vLeNq9qi9LNmc=">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</latexit>
où est le tétraèdre de sommets E
<latexit sha1_base64="HSKlGo1ltQhu6Xtl3VAOzLIAyOs=">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</latexit>(3, 0, 0)
<latexit sha1_base64="F8MDOlXSdokrf/7bVh92h+pa7JM=">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</latexit>
(0, 2, 0)
<latexit sha1_base64="sOaMVHCH23MKe/f8tKTjLel/rhk=">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</latexit>
(0, 0, 1)
<latexit sha1_base64="hVwyCZSlWsozz5qa4P+mwUxy2SU=">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</latexit>
0
<latexit sha1_base64="39Lj6fgry/Gsjnl3GCUePDfhfaM=">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</latexit> x 3
La droite passant par (3, 0)
<latexit sha1_base64="iR0R312qjIkuMd6JtPLoFgC707M=">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</latexit>
(0, 2)
<latexit sha1_base64="w6cfsgR7e4HvGpvcyZr1XHLx2wM=">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</latexit>
x
3 + y
2 + z = 1
<latexit sha1_base64="Dvaw3sOt9Ix5R+T54kmuEY+dFWk=">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</latexit>
L’équation du plan = ) z = 1 x
3
y 2
<latexit sha1_base64="UM8Vot8+EI5wf2XijKGQ2eFzn3Y=">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</latexit>
0 z 1 x 3
y 2
<latexit sha1_base64="4OyakRcbrirtXRT5Qh0eYKe+mp0=">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</latexit>
y = 2
3 x + 2
<latexit sha1_base64="IM1orY/n5vyDILMpXfZmq2+hSs8=">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</latexit>
0 y 2
3 x + 2
<latexit sha1_base64="EfCy/7JQQ8+c1kqjgapDC0FR0PU=">AAADPHicjVJNb9QwFJwNFEr52sINLhErJCTEKtkilWMFF45FYttK3apKXG+xmk2C41RdRSvxa7jCL+B/cOcAQlw5M351JaDiw1Gc8byZZ78X53VhGpckH3vRhYtLly4vX1m5eu36jZv91VtbTdVapceqKiq7k2eNLkypx864Qu/UVmezvNDb+dEzH98+1rYxVfnSzWu9N8sOSzM1KnOk9vt3kkmhX8dzPz+aTG2mutGiW1ucPBzt9wfJMJERnwdpAAOEsVmt9pYwwQEqKLSYQaOEIy6QoeGzixQJanJ76MhZIiNxjQVW6G2p0lRkZI84H3K1G9iSa5+zEbfiLgVfS2eM+/RU1Fliv1ss8VYye/ZPuTvJ6c825zcPuWZkHV6R/ZfvTPm/Pl+LwxRPpAbDmmphfHUqZGmlK/7k8U9VOWaoyXl8wLglVuI863MsnkZq973NJP5ZlJ71axW0Lb78tTrvOA47+FN5pRbGSqdO6+zkbxtqa+n6nMhxlv/J25P+flfOg63RMF0bpi8eDzaehnu0jLu4hwe8K+vYwHNsYsxzvMFbvMP76EP0KfoafTuVRr3guY1fRvT9Bx48rVU=</latexit>
Exemple ZZZ
E
xy dV
<latexit sha1_base64="HVvOym2w+/55USwXPrgSADrLLlg=">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</latexit>
(0, 0, 0)
<latexit sha1_base64="lEJbA+jiIF1G8/vLeNq9qi9LNmc=">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</latexit>
où est le tétraèdre de sommets E
<latexit sha1_base64="HSKlGo1ltQhu6Xtl3VAOzLIAyOs=">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</latexit>(3, 0, 0)
<latexit sha1_base64="F8MDOlXSdokrf/7bVh92h+pa7JM=">AAADJ3icjVLLSsNAFD2Nr/p+Ld0Ei6AgJVFBl0U3LitYW1CRJI46mCZhMhFK8SPc6hf4Ne5El+70L7xzO4JafExIcubcc+7MvTNhFstce95zyRkYHBoeKY+OjU9MTk3PzM4d5GmhItGI0jhVrTDIRSwT0dBSx6KVKRG0w1g0w8sdE29eCZXLNNnXnUwct4PzRJ7JKNBENZfXV71Vb+VkpuJVPR5uP/AtqMCOejpbGsIRTpEiQoE2BBJowjEC5PQcwoeHjLhjdIlThCTHBa4xRt6CVIIUAbGX9D2n2aFlE5qbnDm7I1olpleR08USeVLSKcJmNZfjBWc27E+5u5zT7K1D/9DmahOrcUHsX74P5X99phaNM2xxDZJqypgx1UU2S8FdMTt3P1WlKUNGnMGnFFeEI3Z+9NllT861m94GHH9lpWHNPLLaAm+/VmccV3YFsyujFMwo7lSvzi6ftiRtxl3vENL05fOk2+N/vyv94GCt6q9X/b2NSm3b3qMyFrCIZborm6hhF3U0eG83uMWdc+88OI/OU0/qlKxnHl+G8/IODGCkTg==</latexit>
(0, 2, 0)
<latexit sha1_base64="sOaMVHCH23MKe/f8tKTjLel/rhk=">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</latexit>
(0, 0, 1)
<latexit sha1_base64="hVwyCZSlWsozz5qa4P+mwUxy2SU=">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</latexit>
0
<latexit sha1_base64="39Lj6fgry/Gsjnl3GCUePDfhfaM=">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</latexit> x 3 0 z 1 x
3
y 2
<latexit sha1_base64="4OyakRcbrirtXRT5Qh0eYKe+mp0=">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</latexit>
0 y 2
3 x + 2
<latexit sha1_base64="EfCy/7JQQ8+c1kqjgapDC0FR0PU=">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</latexit>
Z
30
Z
23 x+20
Z
1 x3 y20
xy dzdydx
<latexit sha1_base64="jkqN7r15oD5098ACEONFMCkbr/c=">AAADbnicjVJNb9NAEJ3EFNrylYLEBSEsIqRKiMhOkOixggsHDkUibaWmRPZ6067q2NZ6XcW1/Kf4NXCEE73xE3g73UgtFR9r2X775r3ZndmNi1SVJgi+drrejZWbt1bX1m/fuXvvfm/jwW6ZV1rIscjTXO/HUSlTlcmxUSaV+4WW0TxO5V588tbG906lLlWefTR1IQ/n0VGmZkpEBtS0936iMjMNPo3cv3k5melINMO2GbWLF8N2yYcusLABh+sWunZRT/zkLKmTxbTXDwYBD/86CB3okxs7+UZnhSaUUE6CKpqTpIwMcEoRlXgOKKSACnCH1IDTQIrjklpah7eCSkIRgT3B9wizA8dmmNucJbsFVknxajh9eg5PDp0Gtqv5HK84s2X/lLvhnHZvNf6xyzUHa+gY7L98S+X/+mwthma0xTUo1FQwY6sTLkvFXbE79y9VZZChAGdxgrgGFuxc9tlnT8m1295GHP/BSsvauXDais7/Wp11nLoV7K6sUjKjuVMXdTZ82gragrteAxl8+Txxe8Lf78p1sDschKNB+OFVf/uNu0er9Jie0Sbuymvapne0Q2Ps4zN9oW/0vfvTe+Q98Z5eSLsd53lIV4a3+Qt6Fr7c</latexit>
=
Z
30
Z
23 x+20
xy ⇣
1 x 3
y 2
⌘ dydx
<latexit sha1_base64="2iiW2F4gyi2srg10x4pXWGlvUs4=">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</latexit>
=
Z
30
Z
23 x+20
✓
x x
23
◆
y xy
22 dydx
<latexit sha1_base64="U7ByvXHMpoplIORDlmIEuYwZXpY=">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</latexit>
=
Z
30
✓
x x
23
◆ y
22
xy
36
2
3 x+2
0
dx
<latexit sha1_base64="QFS+uFu20hmiZ0yAxjPV4TStD+Q=">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</latexit>
Exemple ZZZ
E
xy dV
<latexit sha1_base64="HVvOym2w+/55USwXPrgSADrLLlg=">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</latexit>
(0, 0, 0)
<latexit sha1_base64="lEJbA+jiIF1G8/vLeNq9qi9LNmc=">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</latexit>
où est le tétraèdre de sommets E
<latexit sha1_base64="HSKlGo1ltQhu6Xtl3VAOzLIAyOs=">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</latexit>(3, 0, 0)
<latexit sha1_base64="F8MDOlXSdokrf/7bVh92h+pa7JM=">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</latexit>
(0, 2, 0)
<latexit sha1_base64="sOaMVHCH23MKe/f8tKTjLel/rhk=">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</latexit>
(0, 0, 1)
<latexit sha1_base64="hVwyCZSlWsozz5qa4P+mwUxy2SU=">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</latexit>
Z
30
Z
23 x+20
Z
1 x3 y20
xy dzdydx
<latexit sha1_base64="jkqN7r15oD5098ACEONFMCkbr/c=">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</latexit>
=
Z
30
✓
x x
23
◆ y
22
xy
36
2
3 x+2
0
dx
<latexit sha1_base64="QFS+uFu20hmiZ0yAxjPV4TStD+Q=">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</latexit>
=
Z
30
✓
x x
23
◆
23
x + 2
22
x
23x + 2
36 dx
<latexit sha1_base64="RcpmgJwytlBlHtET9OE4LtceNwY=">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</latexit>
= 1 6
Z
30
3x x
2✓ 2
3 x + 2
◆
2x
✓ 2
3 x + 2
◆
3dx
<latexit sha1_base64="qVALA9j1o+cysecUZXzAv/n8ByI=">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</latexit>
= 1 6
Z
30
3x x
2✓ 4
9 x
28
3 x + 4
◆
x
✓ 8
27 x
3+ 8
3 x
28x + 8
◆
dx
<latexit sha1_base64="7k+CN23U2TrDajDMk0VaBidh84E=">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</latexit>