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High Level Math
Integration
Definite integral
Second fundamental theorem of calculus
ā«
a
b
f
(
x
)
d
x
=
F
(
b
)
ā
F
(
a
)
\int_a^b f(x) dx = F(b) - F(a)
ā«
a
b
ā
f
(
x
)
d
x
=
F
(
b
)
ā
F
(
a
)
Where
F()
is the anti-derivative of
f()
ā«
a
b
x
2
d
x
=
[
x
3
3
]
a
b
=
b
3
3
ā
a
3
3
\begin{align*} \int_a^b x^2 dx &= [\frac{x^3}{3}]_a^b \\ \\ &= \frac{b^3}{3} - \frac{a^3}{3} \end{align*}
ā«
a
b
ā
x
2
d
x
ā
=
[
3
x
3
ā
]
a
b
ā
=
3
b
3
ā
ā
3
a
3
ā
ā
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Properties of definite integral
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Multi-method for solving definite integral
Last updated
5 years ago
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