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NDA 1 2024 Maths, question 77

Topic: Integral calculus

Q77

Let p=∫abf(x)dxp=\int _{a}^{b}f(x) dx and q=∫ab∣f(x)∣dxq=\int _{a}^{b}|f(x)| dx. If f(x)=e−xf(x)=e^{-x}, then which one of the following is correct ?

  1. (a) p=2qp=2q
  2. (b) p=−qp=-q
  3. (c) 4p=q4p=q
  4. (d) p=qp=qCorrect answer

Solution.

Answer: (d) p=qp=q

  1. The exponential e^(−x) is positive for every real x, so |f(x)| = f(x) pointwise.
  2. The two integrals with the same limits are equal: p = q.