COMEDK · Maths · 30. Definite Integration
\(\int_{-2}^2 \dfrac{|x-3|}{x-3} d x=\)
- A \(-4\)
- B \(-2\)
- C \(0\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(-4\)
Step-by-step Solution
Detailed explanation
The integrand is \(f(x) = \dfrac{|x-3|}{x-3}\). Recall the definition of the absolute value function: \(|x-3| = x-3\) if \(x-3 > 0\) (i.e., \(x > 3\)) and \(|x-3| = -(x-3)\) if \(x-3 < 0\) (i.e., \(x < 3\)). For the interval \([-2, 2]\), we have \(x < 3\) for all \(x\) in the…
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