Class CBSE Class 12 Mathematics Definite Integrals Q #633
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
\(\int_{a}^{b}f(x)dx\) is equal to:
(A) \(\int_{a}^{b}f(a-x)dx\)
(B) \(\int_{a}^{b}f(a+b-x)dx\)
(C) \(\int_{a}^{b}f(x-(a+b))dx\)
(D) \(\int_{a}^{b}f((a-x)+(b-x))dx\)
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Step-by-Step Solution

  1. Recall the property of definite integrals: \(\int_{a}^{b}f(x)dx = \int_{a}^{b}f(a+b-x)dx\)
  2. Compare the given options with the property.
  3. Option (A): \(\int_{a}^{b}f(a-x)dx\) - Incorrect.
  4. Option (B): \(\int_{a}^{b}f(a+b-x)dx\) - Correct, as it matches the property.
  5. Option (C): \(\int_{a}^{b}f(x-(a+b))dx\) - Incorrect.
  6. Option (D): \(\int_{a}^{b}f((a-x)+(b-x))dx = \int_{a}^{b}f(a+b-2x)dx\) - Incorrect.

Correct Answer: \(\int_{a}^{b}f(a+b-x)dx\)

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires the student to recall and comprehend a property of definite integrals.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the properties of definite integrals, which falls under conceptual knowledge. Specifically, the property \(\int_{a}^{b}f(x)dx = \int_{a}^{b}f(a+b-x)dx\) needs to be understood and applied.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the knowledge of a standard property of definite integrals as covered in the textbook.

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