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intefrated the function f(x) on R if f(x) =sinx.sin2x.sin3x.dx intefrated the function f(x) on Rif f(x) =sinx.sin2x.sin3x.dx
Dear StudentLetI=∫sinx.sin2x.sin3xdx=(1/2) ∫2sinx.sin2x.sin3xdx= (1/2) ∫sinx.(2sin2x.sin3x)dxWe know that[2sinA.sinB=cos(A−B)−cos(A+B)]So,= (1/2)∫sinx.(cosx−cos5x)dx=(1/2)(1/2)∫2sinx.cosxdx−2×21∫2sinx.cos5xdx= (1/4) ∫sin2xdx−(1/4)∫(sin6x−sin4x)dx=− (1/8)cos2x+(1/24)cos6x−(1/16)cos4x+cThanks
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