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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 |
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by
applying the chain rule |
F(g (x))' =
F' (g (x)) g' (x) = f
(g
(x)) g' (x) . |
Thus,
obtained is substitution rule |
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Evaluating
indefinite integrals using substitution rule, examples
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Evaluate
the following indefinite integrals using substitution rule |
31. |
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32. |
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33. |
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34. |
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35. |
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36. |
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37. |
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38. |
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Evaluating the indefinite integrals using substitution rule,
solutions
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Example:
31.
Evaluate |
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Example:
32.
Evaluate |
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Example:
33.
Evaluate |
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Solution:
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Let's show that given
integral is similar to that solved in the example 31. |
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Example:
34.
Evaluate |
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Example:
35.
Evaluate |
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Example:
36.
Evaluate |
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Example:
37.
Evaluate |
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Solution:
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Let's show that given
integral is similar to that solved in the above example 36. |
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Example:
38. Evaluate |
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