Calculus 6.2

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Integration bySubstitution
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The chain rule allows us to differentiate a wide
variety of functions, but we are able to find
antiderivatives for only a limited range of
functions? We can sometimes use substitution or
change of variable to rewrite functions in a form
that we can integrate.
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Example 1
The variable of integration must match the
variable in the expression.
Dont forget to substitute the value for u back
into the problem!
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Example 2
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Example 3
Solve for dx.
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Example 4
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Example 5
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Example 6
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Example 7
We can find new limits, and then we dont have to
substitute back.
We could have substituted back and used the
original limits.
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Example 7 continued
Using the original limits
Wrong! The limits dont match!
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Example 8
Dont forget to use the new limits.
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Acknowledgement I wish to thank Greg Kelly from
Hanford High School, Richland, USA for his hard
work in creating this PowerPoint. http//online.m
ath.uh.edu/ Greg has kindly given permission for
this resource to be downloaded from
www.mathxtc.com and for it to be modified to suit
the Western Australian Mathematics Curriculum.
Stephen Corcoran Head of Mathematics St
Stephens School Carramar www.ststephens.wa.edu.
au
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