Class CBSE Class 12 Mathematics Integrals Q #802
COMPETENCY BASED
APPLY
1 Marks 2023 MCQ SINGLE
∫ from -1 to 1 [|x-2| / (x-2)] dx, x≠2 is equal to
(A) 1
(B) -1
(C) 2
(D) -2
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Step-by-Step Solution

**Step 1: Analyze the integrand** The integrand is |x-2| / (x-2). Since x ≠ 2, we can analyze the behavior of this function. - If x > 2, then |x-2| = x-2, so |x-2| / (x-2) = 1. - If x < 2, then |x-2| = -(x-2), so |x-2| / (x-2) = -1.
**Step 2: Apply the analysis to the given integral** The integral is from -1 to 1. Since the entire interval [-1, 1] is less than 2, we have |x-2| / (x-2) = -1 for all x in [-1, 1].
**Step 3: Evaluate the integral** ∫ from -1 to 1 [|x-2| / (x-2)] dx = ∫ from -1 to 1 (-1) dx = - ∫ from -1 to 1 dx = - [x] from -1 to 1 = - (1 - (-1)) = - (1 + 1) = -2.

Correct Answer: -2

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to apply their understanding of definite integrals and absolute value functions to solve the problem. They need to break down the integral based on the properties of the absolute value function.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of absolute value functions within an integral and how to handle them. It requires understanding the behavior of |x-2| and how it affects the integral over different intervals.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question requires application of the concepts of definite integrals and absolute value functions, going beyond simple recall and application of formulas.

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