[DTube] Reduction Formula for Integral of ∫sin^n(x)dxsteemCreated with Sketch.

in dtube •  6 years ago  (edited)


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In this video, we work through the derivation of the reduction formula for the integral of sinn(x) or [sin(x)]n.

We can approach this problem with integration by parts. The first step is to rewrite the integral as:

∫sinn(x)dx = ∫sinn-1(x)sin(x)dx

Thus we have 2 parts to the integral, where:

u = sinn-1(x)
dv = sin(x)dx

We can then proceed with integration by parts:

∫udv = uv - ∫vdu

Working through the substitutions and the steps, we eventually arrive at the reduction formula shown in the video.


Integration: Reduction Formulas

  1. Reduction Formula for Integral of ∫sin^n(x)dx
  2. Reduction Formula for Integral of ∫cos^n(x)dx
  3. Reduction Formula for Integral of ∫tan^n(x)dx

Thanks for watching. Please give me a "thumbs up" if you have found this video helpful.

Please ask me a maths question by commenting below and I will try to help you in future videos.


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