LISTA DE CÁLCULO - INTEGRAIS TRIPLAS

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1) Calcule onde R = 2) Calcule sen(x + y + z) dr dy dz, onde R = [0, =] [0, 3) Calcule + + + z) dr dy dz, onde R = [0, 1] [0, 1] 1]. 4) Calcule I = 4-z dydr dz 4 5) Calcule 6) Calcule 7) Calcule 8) Calcule 9) Calcule[0,1] [1,2] + [0,3] So So' I So' xyz = 1.' 1/2 yz II 2 dy 1/2 2 2 : A - 4 1 3 4 4 = 8 0 27 u.v 8 2 sen dy dz I 3) : x+y+z So" du = + I as dy u, y+z du, = 1dy -sen 3) + (y+z) - + 3) + sen sen - = - +3) + 2 an (3) 3) + - sen dz (H+3) : dz sen du - sen dz C 3) - + 2 - + + -2-1 1 -2 -1 = -83 + xyz) dr dy dz= = = [0,1], [0,1] So + + xy do dy dz I So = + z + 2 1: 0 3 1/3 + y2+ + + 1/2 3 II 3 + + + 1/2 2 3 y + + + 4 ! 3 1 + 1 3 + + 1 4 = 3 2 + + 1 4 111 So 4 z dz = 3 + 3 + 8 = 3 2 1 1/3 + = 24 = 00/10 8 4 So So dy dz = 4-z So x (2z) dy = son y = sen 4- So sen 4-3 (2z) x = son 4 (2z) 2 14-8 = sen = (2z) 2 sen (2z) 2 2 So sen 2 dz du = 2z = 1. 2 4 sin du 2 1. 4 cos 0 = 4 4 too (8) + 1 4 + 1 4 4 5 So + 32) dy dz 3 + y + = 3 + ya So 3 32 = 1/3 3 y + 3 + y 2 3 2 3 + 3 + 2 3 2 10 3 + 0 3 10 3 + 2 = 10 3 z + 2 3 8 : 30 3 + 2. (27) = 3 6 dr dy = = 3 y = 3 y 3 y = 3 2 3 3 3 2 9 + 2 = 9 4 4.33 3 3 -1 = 27 4 + 27 4 277 So So dz dy dx = = x2y = 1.x 0 2 2 2 dx = = 1 u.v 10 10 8 sen y dz dr sen dz = = seny Sot y of y = y = sen (g) - cos(g) 2 4 1 X " g Calcule -2 So So dz dy So dz = 5 5 5 = = 208 30 30 x8 dr = : 1 + 512 = 57 u.v. 30 270 270 270 270:9 30