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AP EAMCET20225 Jul 2022Morning ShiftMathematicsDefinite IntegrationActual

₁^3 x^n x^2-1 d x=6 , then n=

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct answer

B. 3

Step-by-step solution

Let I= ₁^3 x [n] x^2-1 d x=6= 1 2 ₁^3 2 x (x^2-1 )^ 1 n d x=6 [ (n^2-1 )^ 1 n +1 1 n +1 ]₁^3=12 (8)^ 1 n +1 1 n +1 =12 (8)^ 1 n (n+1) (n)= 3 2 Now, on putting n=3 , L H S = R. H S n=3

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