Best Answer

∫sin2x dx

Use the identity sin2x = ½ - ½(cos2x)

∫[½ - ½(cos2x)] dx = ∫½ dx - ∫½(cos2x) dx

Let's split it up into ∫½ dx and ∫½(cos2x) dx

∫½ dx = x/2 (we'll put the constant in at the end)

∫½(cos2x) dx (Use u substitution with u=2x and du = 2 dx)

∫cosu ¼du = ¼∫cosu du = ¼sinu + c = ¼sin2x (remember to resubstitute)

Subtract the two parts and add a constant

x/2 - ¼(sin2x) + c

This is also equivalent to: ½(x - sinxcosx) + c

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Q: What is the antiderivative of sine squared?

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It is 1.

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Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).

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The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.

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A sine wave is a mathematical function that describes a smooth repetitive oscillation which looks like a wave going from 1 to -1 and back to 1. A normal sine wave is much like a sine wave but has been normalized for practical uses like in electronics creating a "squared" sine wave A perfect sine wave does not exist in reality, it only exists in the minds of mathematicians.

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