# What is the integral of #sin^2(x)cos^4(x) #?

We will use the following Identities to simplify the Integrand :-

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The integral of (\sin^2(x)\cos^4(x)) can be computed using trigonometric identities and integration techniques. Here's how to do it:

- Use the identity (\sin^2(x) = 1 - \cos^2(x)) to rewrite the integral as ((1 - \cos^2(x))\cos^4(x)).
- Expand the expression to get (\cos^4(x) - \cos^6(x)).
- Split the integral into two parts: (\int \cos^4(x) , dx) and (\int \cos^6(x) , dx).
- For (\int \cos^4(x) , dx), use the reduction formula (\int \cos^n(x) , dx = \frac{\cos^{n-1}(x)\sin(x)}{n} + \frac{n-1}{n}\int \cos^{n-2}(x) , dx).
- For (\int \cos^6(x) , dx), use a similar reduction formula.
- After integrating both parts, combine the results to find the integral of (\sin^2(x)\cos^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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