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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 |
11. |
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12. |
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13. |
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14. |
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15. |
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16. |
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17. |
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18. |
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19. |
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20. |
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Evaluating the indefinite integrals using substitution rule,
solutions
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Example:
11.
Evaluate |
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Example:
12.
Evaluate |
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Example:
13.
Evaluate |
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Example:
14.
Evaluate |
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Example:
15.
Evaluate |
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Example:
16.
Evaluate |
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Example:
17.
Evaluate |
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Example:
18.
Evaluate |
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Example:
19.
Evaluate |
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Example:
20.
Evaluate |
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