Integration by substitution

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Integration by substitution
Adrian Sparrow
www.ibmaths.com
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Try integrating
Hint Try a guess and differentiate it.
Answer
That was easy to guess, but lets try it with
substitution
Let
So we have
(the dx is a problem)
So,
Thats a simple one . now lets try a harder one
..
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Try this integral
so,
and
Re-write your integral
Integrate and then substitute
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Now try some of your own (about 10 minutes).
1. 2. 3. 4. 5.
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What about definite integration?
Take the upper and lower values of x from the
integral and find the corresponding values of u.
Now re-write the integral in terms of u, as you
did before.
Confirm this result by using your GDC.
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Now some of your own (about 10 minutes).
1. 2. 3.
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One step beyond.
Try this one-
(too easy!)
Something wrong? - That x, but .
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A couple of special cases part 1
Let xsinu
so,
but remember
so,
Now try
and
and finally conjecture for
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A couple of special cases part 2
and
remember
now try
and
and finally conjecture for