# How do you find the integral of #sin^2(2x) dx#?

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To find the integral of sin²(2x) dx, you can use the double angle identity for sine, which states that sin²(2x) = (1 - cos(4x))/2. Then integrate this expression with respect to x. The integral of (1 - cos(4x))/2 dx can be computed by integrating each term separately. The integral of 1/2 dx is (1/2)x, and the integral of cos(4x) dx can be found using a simple substitution. Once you find the integrals of each term, combine them to get the final result.

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To find the integral of (\sin^2(2x) , dx), you can use the trigonometric identity (\sin^2(x) = \frac{1}{2} - \frac{1}{2}\cos(2x)). Applying this identity to the integral, you get (\int \sin^2(2x) , dx = \int \left(\frac{1}{2} - \frac{1}{2}\cos(4x)\right) , dx). Now integrate each term separately: (\int \frac{1}{2} , dx) and (\int \frac{1}{2}\cos(4x) , dx). Integrating, you get (\frac{1}{2}x - \frac{1}{8}\sin(4x) + C), where (C) is the constant of integration. Therefore, the integral of (\sin^2(2x) , dx) is (\frac{1}{2}x - \frac{1}{8}\sin(4x) + C).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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