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f(x, y, z) = x 2 +y 2 +z 2 x+y+z+1 =
0
f(x, y, z) = (x + y + z) 2 x 2 + 2y 2 + 3z 2 = 1
f(x, y, z) = x2 + cos(y)
≤ 10}.
C = {(x, y, z) ∈ R3 : x2 + y2 + ez2 f(x, y, z) = y √ 1 + z2 C = {(x, y, z) ∈ R3 : x2 − 2x + y2 + z2 ≤ 3}
f(x, y, z) = (1 + x2 )ez2 C = {(x, y, z) ∈ R3 : x2 + y4 − 2y2 + z2 ≤ 0}
f(x, y) = cos2 (x)+y 3 −3y2
Q = {(x, y) ∈ R2 : −π < x < 2π, |y| < 3π}
a ∈ R
fa(x, y, z) = x + ax2 − cos(y) + z2ex C = {(x, y, z) ∈ R3 : 0 ≤ x ≤ 2, −π ≤
y ≤ π, −1 ≤ z ≤ 1}
a ∈ R
fa(x, y, z) = ea cos(z)+y2
+ sin 2 (x) C = {(x, y, z) ∈ R 3 : |y| ≤ 1}
D x2 + y2 dx dy D D
2 3
x D
2
x2 +y2 dx dy D
y = x y = −x x = 1
D = {(x, y) ∈ R2 : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}
y
1 + xy dxdy
D
D = B((0, 0), 3) \ B((0, 0), 2) ∩ {y ≥ 0}
x2 + y2 dxdy
D
D = B((1, 0), 1) \ B((0, 0), 1) ∩ {y ≥ 0}
x
D
2 + y 2 dxdy
x sin |y − 2x| dx dy
D (0, 0) (1, 0) (0, 1)
D 0 ≤ x ≤ 1 0 ≤ y ≤ 1
R 2
D
D
1
x + y dxdy
1
(1 + x 2 )(1 + y 2 ) dxdy
T
z 1 − y 2 dx dy dz,
T 1 z
1