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AP EAMCET202319 May 2023Morning ShiftMathematicsDefinite IntegrationActual

If S_n= ₀^ 2 (2 n-1) x x d x and n is an integer, then S _ n +1 - S _ n =

Options

  1. A- 2
  2. B1
  3. C0
  4. D2

Correct answer

C. 0

Step-by-step solution

S_n= ₀^ / 2 (2 n-1) x x d x (given) Hence S_ n+1 = ₀^ / 2 (2 n+1) x x d x Replacing 'n' by (n+1) Therefore aligned S_ n+1 -S_n & = ₀^ / 2 [ (2 n+1) x- (2 n-1) x] x d x S_ n+1 -S_n & = ₀^ / 2 2 2 n x x x d x & C- D =2 C+D 2 C-D 2 aligned aligned S_ n+1 -S_n & = 1 n [ 2 n x]₀^ / 2 = 1 n [ n - 0] & =0 Since n is an integer aligned

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