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xz 3 dx dy dz,
T
T y =
4x2 + 9z2 y = 1
e
T
(x2 +y2 +z2 ) 3/2
T 4x2 + y2 + z2 ≤ r2
dx dy dz,
(x
T
2 + y 2 ) dx dy dz,
T z
r z = h
D := {(x, z) ∈ R 2 : x 2 + z 2 ≤ 2, x 2 + (z − 1) 2 ≥ 1, z ≥ 0}
D
D + := {(x, z) ∈ D : x ≥ 0}
S D
z
I = [0, 1] α ∈ R fα : I × I → R
0 x = y
fα(x, y) =
1
|x−y| α
x = y
α fα I × I α
fα(x, y) dx dy
I×I
D := {(x, y) ∈ R 2 : (x + y) 2 ≤ e −(x−y)2
I =
}
e −(x−y)2
dxdy
D
z = arcsin x
(x, y) D y2 = x2 (1 −
x2 )
x2 + y2 − z2 = 0
x ≥ 0 y ≥ 0 z ≥ 0 x + y + z ≤ 1
γ ρ = Aθ θ ∈ [0, 4π]
I := θ 3 ds.
x(θ) = ρ(θ) cos θ = Aθ cos θ
y(θ) = ρ(θ) sin θ = Aθ sin θ
ϕ(θ) = (x(θ), y(θ))
˙x A cos(θ) − Aθ sin(θ)
Jac ϕ(θ) = =
˙y A sin(θ) + Aθ cos(θ)
γ