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Comprehension

Direction : Consider the following for the items that follow :

Let f(x) = |x2 - x - 2|

What is \(\rm \int_0^2f(x)dx\) equal to

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 0
  2. 1
  3. 5/3
  4. 10/3

Answer (Detailed Solution Below)

Option 4 : 10/3
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Detailed Solution

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Explanation:

Given:

f(x) =|x2 – x – 2|.

= {x2 – x – 2; x ∈ (-∞ –1) ∪  (2,∞ ) – (x2 – x – 2); x ∈ [–1, 2]

Let I = - \(\int_0^2(x^2 – x – 2)dx\)

= - \([\frac{x^3}{3}-\frac{x^2}{2} -2x]_2^0\)

= \(- [\frac{8}{3}-\frac{4}{2}+4] +0 =\frac{10}{3}\)

∴ Option (d) is correct

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