
#1
Jan2511, 12:52 AM

P: 1

1. The problem statement, all variables and given/known data
∫〖Sin^(2 ) x * cos2x dx〗 2. Relevant equations The right answer should be: sin 2x / 4  x/4  sin4x / 16 3. The attempt at a solution If i would set Sin^(2 ) x= (1cos2x)/2 I can replace it in the integral Then we get: ∫▒〖(1cos2x)/2 cos2x dx〗 As far as I am concerned we cannot use the constant multiple rule because there is no constant to multiply I don’t know how to go on from here to solve it 



#2
Jan2511, 01:14 AM

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P: 11,521

OK, so you have
[tex]\begin{align*} \int \sin^2 x\cos 2x\,dx &= \int\left(\frac{1\cos 2x}{2}\right)\cos 2x\,dx \\ &= \frac{1}{2}\int(\cos 2x  \cos^2 2x)\,dx \\ &= \frac{1}{2}\int\cos 2x\,dx  \frac{1}{2}\int \cos^2 2x\,dx \end{align*}[/tex] Can you take it from there? Hint: use a trig identity for cos^{2} 2x. 


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