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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Definite Integration

NDA 2018 · Mathematics · Definite Integration

What is ∫_a^b[x] d x+∫_a^b[-x] d x equal to, where[.] is the...

What is ∫ab[x]dx+∫ab[−x]dx\int_a^b[x] d x+\int_a^b[-x] d x equal to, where[.] is the greatest integer function?

Options

  1. Ab-a
  2. Ba-b
  3. C0
  4. D2(b-a)

Correct answer

B. a-b

Step-by-step solution

∫ab[x]dx+∫ab[−x]dx=∫ab([x]+[−x])dx=∫ab(−1)dx=a−b\begin{aligned} & \int_a^b[x] d x+\int_a^b[-x] d x \\ & =\int_a^b([x]+[-x]) d x=\int_a^b(-1) d x=a-b\end{aligned}
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