Integrals of the product of the powers of sine and cosine come in 4 permutations:
1. The powers m and n are both even
2. The powers m and n are even and odd respectively
3. The powers m and n are odd and even respectively
4. The powers m and n are both odd
In this video, we explore case 1 where both powers are even. In this case, our aim is to reduce the powers to the first power of cosine, so that we have…
sin^m(x)*cos^n(x) = A + B*cos(2x) + C*cos(4x) + D*cos(6x) +…
We can get the integrand into this form using the power reducing half-angle formulas and the product-to-sum formulas.
We look specifically at the example of the integral of sin^4(x)*cos^2(x).
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