# How do you find the integral of #int sin^(2)t cos^(4)t #?

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To find the integral of ( \int \sin^2(t) \cos^4(t) ), you can use trigonometric identities to simplify the integral. One common approach is to use the power-reducing formulas for sine and cosine, which express higher powers of sine and cosine in terms of lower powers and/or other trigonometric functions.

The power-reducing formula for sine is ( \sin^2(t) = \frac{1}{2}(1 - \cos(2t)) ), and for cosine is ( \cos^2(t) = \frac{1}{2}(1 + \cos(2t)) ).

Using these identities, you can rewrite the integrand ( \sin^2(t) \cos^4(t) ) in terms of cosine only. Then, you can use a substitution or direct integration techniques to find the integral.

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