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NDA 2024 · PYQ · Definite Integration · easy

Let p = ∫_a^b f(x) dx and q = ∫_a^b |f(x)| dx. If f(x) = e^(-x), then which one of the following is correct?

  1. A.p = 2q
  2. B.p = -q
  3. C.4p = q
  4. D.p = q✓ Correct

Explanation

Since e^(-x) > 0 for all real x, |e^(-x)| = e^(-x). Therefore |f(x)| = f(x), which gives ∫_a^b |f(x)| dx = ∫_a^b f(x) dx, so p = q.
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