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NDA 1 2024 Maths, question 100

Topic: Integral calculus

Passage · Q99 to Q100

Let 3f(x)+f(1x)=1x+13f(x)+f\left( \frac{1}{x} \right)=\frac{1}{x}+1

Q100

What is 8∫12f(x)dx8\int _{1}^{2}f(x) dx equal to ?

  1. (a) ln⁡(8e)\ln (8\sqrt{e})Correct answer
  2. (b) ln⁡(4e)\ln (4\sqrt{e})
  3. (c) ln⁡2\ln 2
  4. (d) ln⁡2−1\ln 2-1

Solution.

Answer: (a) ln⁡(8e)\ln (8\sqrt{e})

  1. Use 8f(x) = 3/x − x + 2.
  2. Integration from 1 to 2 gives 3 ln 2 − 3/2 + 2 = 3 ln 2 + 1/2 = ln(8√e).