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AP EAMCET202422 May 2024Morning ShiftMathematicsDefinite IntegrationActual

_ n ( 1 n^2 + 1 n^2-1 + .+ 1 n^2-(n-1)^2 )=

Options

  1. A2
  2. B2
  3. C2
  4. D3 2

Correct answer

C. 2

Step-by-step solution

aligned & _ ( 1 n^2 + 1 n^2-1 + + 1 n^2-(n-1)^2 ) & = _ n 1 n (1+ 1 1- 1 n^2 + + 1 1- (n-1)^2 n^2 ) & = _ n 1 n _ r=0 ^ n-1 1 1- ( r n )^2 & = ₀^1 d x 1-x^2 = [ ⁻¹ x ]₀^1= 2 . aligned

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