What method has been used in this solved integration problem?

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The integration problem discussed involves the definite integral of τsin(ωτ) from τ=0 to t, resulting in the expression -t/ω(cos(ωt)) + (1/ω^2)(sin(ωt)). The method used to solve this integral is integration by parts, where u=τ and dv=sin(ωτ)dτ. The alternative approach presented by a participant yields a different result, indicating a potential misunderstanding of the integration by parts technique.

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limits from τ=0 to t

∫τsinωτ dτ

answer: [-τ/ω + 1/ω^2(sinωτ] limits τ = 0 to t

= -t/ω(cosωt) + 1/ω^2(sinωt)Could someone please explain the steps? is this an integration by parts method??

when i attempt integration by parts, with u = τ & dv = sin(ωτ) dτ

I get the following answer:

τ(ωcosωτ) - sinωτ
 
Last edited:
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So, you are saying that v = w*cos(w*t). Have you checked this by taking the derivative?

RGV
 

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