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If f'(x)=sin^2(2x), how to find the function f(x)?
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To determine the primitive function f(x), we'll have to evaluate the indefinite integral of the function (sin 2x)^2.
We'll apply the half angle identity:
(sin 2x)^2 = (1 - cos 4x)/2
We'll evaluate the indefinite integral:
Int (sin 2x)^2dx = Int (1 - cos 4x)dx/2
We'll apply the property of integral to be additive:
Int (1 - cos 4x)dx/2 = Int dx/2 - Int cos 4x dx/2
Int (1 - cos 4x)dx/2 = x/2 - sin 4x/8 + C
The primitive of the given function is: f(x)=x/2 - sin 4x/8 + C.
Posted by giorgiana1976 on May 2, 2011 at 3:43 PM (Answer #1)
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