# How do you find the antiderivative of #sin^4(x)#?

You could apply double angle power reduction formulas.

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To find the antiderivative of ( \sin^4(x) ), you can use the power-reducing formula for sine raised to an even power:

[ \sin^2(x) = \frac{1}{2} - \frac{1}{2} \cos(2x) ]

Using this formula twice, you get:

[ \sin^4(x) = \left(\frac{1}{2} - \frac{1}{2} \cos(2x)\right)^2 ]

Expand and simplify this expression. Then integrate term by term. You'll eventually get the antiderivative of ( \sin^4(x) ).

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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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