power reduction formula for the integral of sin^n(x)

[@kshitizmangalbajracharya9451]

There's something called "Reduction Formulae" in (really) old European textbooks on Integral Calculus. It's still there in undergraduate Calculus course in Nepal and probably in many parts of India. The topic basically deals with such integrals and many other similar integrals where we need to reduce the power. It can also involve two powers out of which only one is reduced. Two or more powers are also possible, obviously.

[@cycklist]

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[@silsilatube7627]

It is a briliant way

[@holyshit922]

... and rewrite it into the sum Without reduction Substitute u=Pi/2-x to get cosine Calculate coefficients of Chebyshov polynomial of degree n Put nonzero coefficients of Chebyshov polynomials of degree k where k is natural number not grater then n which gives the same rest in division by 2 as n gives columnwise in the matrix Inverse that matrix Now you can integrate, but integration is very easy

[@evwerenisaacoghenenyerhovw232]

Sir please when are we to use the power reducing formula?? Like I'm just confused

[@AbishekR-ue5zn]

You can use it whenever you have sin^n(x) form, we particularly use this because as we go to larger and larger parts of n, using half angles will be very hard

[@يوسفعمارنة-ش9ت]

W video

[@mandandikaliyes847]

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[@LucienneMakamte]

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[@alanaduarte_]

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