A Change of Variables
Date: 05/05/2003 at 01:12:07 From: Desire Subject: Trigonometric identities How do I solve int(sin^5(2x)cos(2x)dx)?
Date: 05/05/2003 at 03:40:57 From: Doctor Luis Subject: Re: Trigonometric identities Hello, You are solving the following integral: / | | (sin(2x))^5 * cos(2x) dx | / One important thing to notice right away is that the derivative of the sin(2x) is cos(2x), and that is the key to solving this problem (a simple change of variables). As you might have guessed, the simplest substitution you can make is u = sin(2x), which will give you du = 2*cos(2x)dx After substituting your change of variable from x to u, the integral looks like this: / | | u^5 * (du/2) | / Note that I substituted u for sin(x), and du/2 for cos(2x)dx. This should be a form that you can integrate more easily. Let us know if you have more questions. - Doctor Luis, The Math Forum http://mathforum.org/dr.math/
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