Question
Download Solution PDFComprehension
Direction : Consider the following for the items that follow :
Let f(x) = |x2 - x - 2|
What is \(\rm \int_h^3f(x)dx\) equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
f(x) =|x2 – x – 2|
= {x2- x - 2; x ∈ (-∞, -1) ∪ (2, ∞)
- (x2 -x -2 ; x ∈[ -1,2]
Let I = \(\int_1^3f(x)dx\)
= \(- \int_1^2(x^2 -x-2)dx+ \int_3^2(x^2-x-2)dx\)
= \(- [\frac{x^3}{3} -\frac{x^2}{2}-2x]^2_1 + [\frac{x^3}{3} -\frac{x^2}{2}-2x]^3_2\)
= \([\frac{8}{3}-\frac{4}{2}-4] + [[\frac{1}{3}-\frac{1}{2}-2] + [\frac{27}{3}-\frac{9}{2}-6] - [\frac{8}{3}-\frac{4}{2}-4] \)
= \(\frac{20}{6} - \frac{13}{6} -\frac{9}{6} +\frac{20}{6}\) = 3
∴ Option (b) is correct.
Last updated on May 30, 2025
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