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Topic: Re: Trig Subs
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Posts: 10,730
Registered: 12/3/04
Re: Trig Subs
Posted: Sep 27, 1997 8:58 PM
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In a message dated 97-09-27 15:24:33 EDT, wrote

<< On page 12 of the Acorn Book, there is mention of Techniques of
Antidifferentiation. Among the subtopics is "Antiderivatives by substitution
of variables..."

The formulas that you mention result from trigonometric substitutions and I
would guess that they fall into the above catagory.

Yes and No. My reading of the Acorn book is that students should know how to
substitute for the variables in an integral, including, of course, dx and the
limits of integration, But (again my reading) they do not need to memorize a
list of standard substitutions such as those for a^2-x^2, x^2-a^2 and x^2+a^2
-- the "Trig Substitutions." Probably they will be given an integral AND the
substitution to use and asked to do that substitution. This may not be the
usual substitution. For example in the integral Int( SQRT(1 - x^2),x,0 Pi/2)
make the substitution x = cos (theta) pick the correct integral in terms of
(theta) from the multiple choices. Similar problems involving SQRT (x) could
be given.

Lin McMullin
Ballston Spa, NY

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