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Integral
calculus |
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The
indefinite integral |
Substitution rule |
Evaluating the indefinite integrals using substitution
rule examples
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Evaluating the indefinite integrals using substitution
rule
solutions
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Substitution
rule |
Let
f
and g
are differentiable, with range of g
contained in the domain of f,
and let F
be antiderivative of f such
that F'
(u)
= f (u) where u
= g (x), then |
![](SR.gif) |
by
applying the chain rule |
F
(g (x))' =
F' (g (x)) g' (x) = f
(g
(x)) g' (x) . |
Thus,
obtained is substitution rule |
![](SR1.gif) |
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Evaluating
indefinite integrals using substitution rule, examples
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Evaluate
the following indefinite integrals using substitution rule |
1. |
![](SE1.gif) |
2. |
![](SE2.gif) |
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3. |
![](SE3.gif) |
4. |
![](SE4.gif) |
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5. |
![](SE5.gif) |
6. |
![](SE6.gif) |
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7. |
![](SE7.gif) |
8. |
![](SE8.gif) |
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9. |
![](SE9.gif) |
10. |
![](SE10.gif) |
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Evaluating the indefinite integrals using substitution rule,
solutions
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Example:
1.
Evaluate |
![](SE1.gif) |
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Example:
2.
Evaluate |
![](SE2.gif) |
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Example:
3.
Evaluate |
![](SE3.gif) |
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Example:
4.
Evaluate |
![](SE4.gif) |
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Example:
5.
Evaluate |
![](SE5.gif) |
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Example:
6.
Evaluate |
![](SE6.gif) |
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Example:
7.
Evaluate |
![](SE7.gif) |
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Example:
8.
Evaluate |
![](SE8.gif) |
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Example:
9.
Evaluate |
![](SE9.gif) |
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Example:
10.
Evaluate |
![](SE10.gif) |
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