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JEE Main2006MathematicsDefinite IntegrationActual

_ -3 / 2 ^ - / 2 [(x+ )^3+ ^2(x+3 ) ] d x is equal to

Options

  1. A^4 32
  2. B^4 32 + 2
  3. C2
  4. D4 -1

Correct answer

C. 2

Step-by-step solution

I= _ -3 / 2 ^ - / 2 [(x+ )^3+ ^2(x+3 ) ] d x Put x + = t aligned & I= _ - / 2 ^ / 2 [t^3+ ^2 t ] d t=2 ₀^ / 2 ^2 t d t & = ₀^ / 2 (1+ 2 t) d t= 2 +0 . aligned

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