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Lebl-Basic-Analysis-I
· Problem 5.1.1
The Riemann Integral
Mathematics · darboux-sums
Problem
Define
f
:
[
0
,
1
]
→
R
f : [0,1] \to \mathbb{R}
f
:
[
0
,
1
]
→
R
by
f
(
x
)
:
=
x
3
f(x) := x^3
f
(
x
)
:=
x
3
and let
P
:
=
{
0
,
0.1
,
0.4
,
1
}
P := \{0, 0.1, 0.4, 1\}
P
:=
{
0
,
0.1
,
0.4
,
1
}
. Compute
L
(
P
,
f
)
L(P, f)
L
(
P
,
f
)
and
U
(
P
,
f
)
U(P, f)
U
(
P
,
f
)
.
Related theory
Refinement And Monotonicity Of Darboux Sums
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