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NDA2025MathematicsIndefinite IntegrationActual

Consider the following for the two (02) items that follow: Let the function y = (1 - x)⁻¹ , where x 2n and n is an integer. What is y , dx equal to?

Options

  1. A- (x/2) + c
  2. B- (x/2) + c
  3. C(x/2) + c
  4. D(x/2) + c

Correct answer

B. - (x/2) + c

Step-by-step solution

Given y = (1 - x)⁻¹ y = 1 1 - x Using the half-angle formula 1 - x = 2 ^2(x/2) y = 1 2 ^2(x/2) = 1 2 ^2(x/2) Integrating with respect to x : y , dx = 1 2 ^2(x/2) , dx y , dx = 1 2 ( - (x/2) 1/2 ) + c y , dx = - (x/2) + c Answer: - (x/2) + c

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