Несобственные интегралы и интегралы, зависящие от параметров - 52 стр.

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ЮФУ | Ростов-на-Дону

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F (y) =
2y
Z
y
sin(xy)
x
dx F (y) =
y
2
Z
3y
e
x
2
y
dx
F (y) =
ye
y
Z
ye
−y
ln(1 + x
2
y
2
)dx F (y) =
sin y
Z
cos y
sh(x
2
y)dx
f ∈ C(R) F (y) =
1
2a
a
Z
−a
f(x + y)dx
R R
f ∈ C(Π) Π = [a; b] × [c; d] g ∈ R[a; b]
F (y) =
b
Z
a
f(x, y)g(x)dx [c; d]
f ∈ C(Π) Π = [a; b] × [c; d] g ∈ R[a; b]
F (y) =
b
Z
a
f(x, y)g(x)dx [c; d]
b
Z
a
F (y)dy =
b
Z
a
g(x)dx
d
Z
c
f(x, y)dx
f,
∂f
∂y
∈ C(Π) Π = [a ; b]×[c; d] g ∈ R[a; b]
F (y) =
b
Z
a
f(x, y)g(x)dx [c; d]
I(a) =
π
Z
0
ln(1 − 2a cos x + a
2
)dx I(a) =
π/2
Z
0
ln(a
2
cos
2
x + sin
2
x)dx
+∞
Z
0
sin(xy)
x
√
x
dx (0 ≤ y < +∞)
+∞
Z
1
ln
p
(x
2
+ 1)
x
√
x − 1
dx (0, 1 ≤ p ≤ 10)
+∞
Z
2
dx
x ln
α
x
(1 < α
0
≤ α < +∞)
1/2
Z
0
dx
x |ln x|
α
(1 < α
0
≤ α < +∞)
+∞
Z
1
x
α
e
−2x
dx (1 ≤ α ≤ 3)
+∞
Z
0
xdx
1 + (x − α)
4
(−∞ < α ≤ α
0
< 0)
1
Z
0
x
α
arctg(αx)
√
1 − x
2
dx (−2 < α < +∞)

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