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| Integral
calculus |
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Substitution
and definite integration
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Substitution
and definite integration examples
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Integrations
by parts and the definite integral
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Substitution
and definite integration
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When
we evaluate an indefinite integral of the form
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we
use the substitutions g
(x)
= u and g'(x) dx = du
to obtain
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Therefore,
to evaluate the definite integral using substitution
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or
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Note,
by making substitution the definite integral change the limits of
integration. That is, the new limits of integrations
must correspond to the range of values for u
as we now integrate the simpler integrand f
(u)
from ua
= g (a) to
ub = g
(b).
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Substitution
and definite integration examples
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Evaluate |
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Integrations
by parts and the definite integral
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If
u (x)
and v (x)
are continuous functions with continuous derivatives on [a,
b], then
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| Functions
contents G |
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