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Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

g(n)= ₀^ n^2+n+1 e^ x / 2-[x / 2] ( x 2 - [ x 2 ] ) d(x-[x]) ; n N then g(n)

Options

  1. Ahas minimum value as 1 4 + e
  2. Bhas maximum value as 3- e
  3. Chas minimum value as 3 4 - e 4
  4. Dnone of these

Correct answer

D. none of these

Step-by-step solution

g(n)= ₀^ n^2+n+1 e^ x / 2] x 2 d x = (n^2+n+1 ) ₀^1 e^ (x / 2) x 2 d x= (n^2+n+1 ) ₀^1 e^ x / 2 ( x 2 ) d x=n^2+n+1 [4-2 e^ 1 / 2 ] So, minimum value is 12-6 e

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