Integration of Trigonometric FunctionsDate: 05/28/99 at 09:14:00 From: Corenne Subject: Integration in trigonometry I am having problems with the following question: Integrate sin(x)sin(2x).dx I have tried integration by parts but it has not seemed to work. u = sin(x) u' = -cos(x) v' = sin(2x) v = 0.5cos(2x) 0.5sin(x)cos(2x)-(integral of)[-0.5cos(x)cos(2x).dx] Please help! Thank you, Corenne Date: 05/28/99 at 10:17:50 From: Doctor Wilkinson Subject: Re: Integration in trigonometry Hi, Corenne. Integration by parts is a useful tool, but it's not a magic wand. A good question to ask is "what's the main problem here"? I'd say the main problem is that you have both sin(x) and sin(2x) and they don't mix well. Fortunately, we have a formula for sin(2x) in terms of sin(x) and cos(x). When you do integration involving trig functions, you often need to apply trigonometry and not just calculus. Writing sin(2x) = 2sin(x)cos(x) gives you the integral of 2sin^2(x) cos(x) dx and now things are looking good, since cos(x) is the derivative of sin(x). - Doctor Wilkinson, The Math Forum http://mathforum.org/dr.math/ |
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