Trigonometric Integral by Slick Substitution

by Pablo:

Here's an interesting integral that needs a trigonometric identity and then apply ordinary u-substitution.

At first sight, this integral does not seem like anything we've seen before. However, here we can use a trigonometric identity. This is a trick that you probably used when learned to solve limits involving trigonometric limits.

First of all, we remind ourselves of this basic identity:

If we multiply both sides by -1 and add 1:

If we now multiply both sides by two:

Now, of course, we make the substitution:

So, we end up with the identity:

Replacing this in our integral we get:

Now we use simple u-substitution, this is the easier part:

So, we have:

This is a nice trigonometric trick that is convenient to know.

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Apr 28, 2013
sqrt(sin ^2x )= abs sin x?
by: Anonymous

i think the answer must be +and -

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