Aparticle moves on a straight line with velocity function v(t) = sin ωt cos2ωt. find its position function s = f(t) if f(0) = 0.

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v( t)= sin( ωt) cos^2 ( ωt) 

s(t) = ∫sin(ωt) cos^2 (ωt) dt 

let cos(ωt) = u 

-ωsin(ωt) dt = du 

∫sin(ωt) cos^2 (ωt) dt = -(1/ω)∫u^2 du = -(1/ω)u^3 / 3 + const 

s(t) = -(1/ω)cos^3(ωt) / 3 + const 

s(0) = 0 => const = 1/(3ω) 

s(t) = (1 - cos^3(ωt))/(3ω)