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JEE Main20199 Apr 2019Morning ShiftMathematicsDefinite IntegrationActual

The value of ∫ 0 π / 2 s i n 3 x s i n x + c o s x d x is:

Options

  1. Aπ - 1 2
  2. Bπ - 2 8
  3. Cπ - 1 4
  4. Dπ - 2 4

Correct answer

C. π - 1 4

Step-by-step solution

I = ∫ 0 π 2 sin 3 x sin x   +   cos x d x       . . . i Using property of definite integration ∫ a b f x d x = ∫ a b f a + b - x d x , we get I = ∫ 0 π 2 s i n 3 π 2 - x sin π 2 - x + cos π 2 - x   d x Using sin π 2 - x = cos x   &   cos π 2 - x = sin x , ⇒ I = ∫ 0 π 2 cos 3 x cos x + sin x   d x       . . . i i On adding the equation i   &   i i ⇒ 2 I = &#8

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