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ISI2015-DCG-46

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Let $I=\int (\sin x – \cos x)(\sin x + \cos x)^3 dx$ and $K$ be a constant of integration. Then the value of $I$ is

  1. $(\sin x + \cos x)^4+K$
  2. $(\sin x + \cos x)^2+K$
  3. $- \frac{1}{4} (\sin x + \cos x)^4+K$
  4. None of these
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Let $sin\ x+ cos\ x =t$

$\implies (cos\ x - sin \ x)dx = dt$

$\implies I = -\int t^3 dt = -\frac{t^4}{4}+K = -\frac{ (sin\ x+ cos\ x)^4}{4} +K$

$\therefore$ Option $C.$ is the correct option.
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