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NDA 1 2024 Maths, question 95

Topic: Integral calculus

Passage · Q95 to Q96

Let ∫dxx+1−x−1=α(x+1)32+β(x−1)32+c\int \frac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{\frac{3}{2}}+\beta(x-1)^{\frac{3}{2}}+c

Q95

What is the value of α\alpha ?

  1. (a) 13\frac{1}{3}Correct answer
  2. (b) 23\frac{2}{3}
  3. (c) 11
  4. (d) 43\frac{4}{3}

Solution.

Answer: (a) 13\frac{1}{3}

  1. Rationalisation gives 1/[√(x + 1) − √(x − 1)] = [√(x + 1) + √(x − 1)]/2.
  2. Integrating gives [(x + 1)^(3/2) + (x − 1)^(3/2)]/3 + C.
  3. Hence α = 1/3.