Esercizi svolti di analisi reale e complessa - Dipartimento di ...

T x 2 (y − x 3 )e y+x3
dxdy
T ≡ {(x, y) ∈ R 2 : x 3 ≤ y ≤ 3, x ≥ 1}.
E ≡ {(x, y) ∈ R 2 : y 2 ≤ x 2 (1 − |x|)}
E
E
E
{x > 0}
Sx Sy E
x y
fn : [0, 1] ↦−→ R
fn(x) −→ f(x) ∀x ∈ [0, 1] .
Γn fn Γ f
• L(Γn) ≤ M L(Γ) ≤ M
• L(Γn) ≥ M L(Γ) ≥ M
∃c ∈ R
• e −λ(x4 +y 4 ) c
dxdy = √λ ∀λ > 0 .
R 2
• π√π 2 ≤ c ≤ π√2π 2
lim
r↦→+∞ e−r
B(0,r)
e |x|+|y| dxdy .
R 2
D ≡ {(x, y) ∈ R 2 : x > 0, | log x| ≤ 1, |y − x log x| ≤ 1} .