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NDA 2024 · PYQ · Integration · medium

Let ∫ dx/(√(x+1) - √(x-1)) = α(x+1)^(3/2) + β(x-1)^(3/2) + c. What is the value of β?

Answer

The correct answer is C: 1/3. From the rationalization above, the integral equals (1/3)(x+1)^(3/2) + (1/3)(x-1)^(3/2) + c. So β = 1/3.

  1. A.-2/3
  2. B.-1/3
  3. C.1/3✓ Correct
  4. D.2/3

Explanation

From the rationalization above, the integral equals (1/3)(x+1)^(3/2) + (1/3)(x-1)^(3/2) + c. So β = 1/3.
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