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Formula Sheets
/ Maths
Chapter 20
Definite Integration
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All Maths formulas (PDF)
Properties
Newton–Leibniz rule
Limit as a sum
Standard results
Properties
∫
a
b
f
(
x
)
d
x
=
∫
a
b
f
(
a
+
b
−
x
)
d
x
,
∫
0
a
f
(
x
)
d
x
=
∫
0
a
f
(
a
−
x
)
d
x
∫
−
a
a
f
(
x
)
d
x
=
{
2
∫
0
a
f
(
x
)
d
x
,
0
,
f
even
f
odd
∫
0
2
a
f
(
x
)
d
x
=
{
2
∫
0
a
f
(
x
)
d
x
,
0
,
f
(
2
a
−
x
)
=
f
(
x
)
f
(
2
a
−
x
)
=
−
f
(
x
)
Periodic
∫
0
n
T
f
(
x
)
d
x
=
n
∫
0
T
f
(
x
)
d
x
King's rule example
∫
0
π
/2
sin
n
x
+
cos
n
x
sin
n
x
d
x
=
4
π
Newton–Leibniz rule
d
x
d
∫
g
(
x
)
h
(
x
)
f
(
t
)
d
t
=
f
(
h
(
x
))
h
′
(
x
)
−
f
(
g
(
x
))
g
′
(
x
)
Limit as a sum
n
→
∞
lim
n
1
r
=
1
∑
n
f
(
n
r
)
=
∫
0
1
f
(
x
)
d
x
Standard results
Wallis
∫
0
π
/2
sin
n
x
d
x
=
n
n
−
1
⋅
n
−
2
n
−
3
⋯
×
{
2
π
,
1
,
n
even
n
odd
∫
0
π
/2
ln
sin
x
d
x
=
−
2
π
ln
2
Special functions
∫
a
b
[
x
]
d
x
:
split at integers
;
∫
∣
f
(
x
)
∣
d
x
:
split where
f
=
0
Indefinite Integration
Area Under Curves