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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 |
1. |
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2. |
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3. |
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4. |
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5. |
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6. |
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7. |
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8. |
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9. |
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10. |
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Evaluating the indefinite integrals using substitution rule,
solutions
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Example:
1.
Evaluate |
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Example:
2.
Evaluate |
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Example:
3.
Evaluate |
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Example:
4.
Evaluate |
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Example:
5.
Evaluate |
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Example:
6.
Evaluate |
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Example:
7.
Evaluate |
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Example:
8.
Evaluate |
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Example:
9.
Evaluate |
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Example:
10.
Evaluate |
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