Sin2x Sin 4x Cos 4x Dx The correct option c tan 1 tan2x Explanation sin2x dx sin4x cos4x 2sinx cosx dx sin4x cos4x 2 tanx sec2x 1 tan4x dx Let tan2x t 2tanx
Int sin 4x cos 2x dx 1 16 x sin 4x 4 sin 3 2x 3 c intsin 4x cos 2x dx int sin 2x sin 2x cos 2x dx int 1 2 1 cos2x sin2x 2 2dx We have cos2x 1 sin 2 x sin 4 x cos 4 x is equal to 2 tan 1 tan 2 x C tan 1 x tan 2 x C none of the above tan 1 tan 2 x C
Sin2x Sin 4x Cos 4x Dx
Sin2x Sin 4x Cos 4x Dx
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int 0 pi 4 2sinx cosx sin 4x cos 4x dx Dividing each term by cos 4 x we get I int 0 pi 4 2 sinxcancelcosx cos 4x sin 4x cancelcos 4x 1 dx Let I xsinxcosx sin 4 x cos 4 x dx for x 0 2 Dividing numerator and denominator by cos 4 x
cos2x sin2x 1 cos4x dx We need to evaluate int1 sin 4x sin 2xcos 2x cos 4x dx Let I int1 sin 4x sin 2xcos 2x cos 4x dx Multiply the numerator and the denominator by sec 4
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The correct option c tan 1 tan2x Explanation sin2x dx sin4x cos4x 2sinx cosx dx sin4x cos4x 2 tanx sec2x 1 tan4x dx Let tan2x t 2tanx
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