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COMEDK202510 May 2025Evening ShiftMathematicsIndefinite IntegrationActual

_ x 1 ( x -1)(2 x-3) 2 x^2+x-3 is

Options

  1. A0
  2. B1 10
  3. C1
  4. D- 1 10

Correct answer

D. - 1 10

Step-by-step solution

Let L = _ x 1 ( x -1)(2 x-3) 2 x^2+x-3 . Factor the denominator: 2x^2 + x - 3 = 2x^2 + 3x - 2x - 3 = x(2x + 3) - 1(2x + 3) = (x - 1)(2x + 3) . Substitute the factored form into the limit expression: L = _ x 1 ( x -1)(2 x-3) (x-1)(2x+3) Since x - 1 = ( x - 1)( x + 1) , the expression becomes: L = _ x 1 ( x -1)(2 x-3) ( x -1)( x +1)(2x+3) Cancel the common term ( x -1) : L = _ x 1 2x-3 ( x +1)(2x+3) Evaluate the limit by substituting x = 1 : L = 2(1)-3 ( 1 +1)(2(1)+3) = 2-3 (1+1)(2+3) = -1 2 5 = - 1 10 Answer: - 1 10

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