Class CBSE Class 12 Mathematics Integrals Q #804
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
\int_{0}^{\frac{\pi}{6}}sec^{2}(x-\frac{\pi}{6})dx is equal to :
(A) \frac{1}{\sqrt{3}}
(B) -\frac{1}{\sqrt{3}}
(C) \sqrt{3}
(D) -\sqrt{3}
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AI Tutor Explanation

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Step-by-Step Solution

  1. Step 1: Recognize the integral.

    The integral of sec2(x) is tan(x). Therefore, the integral of sec2(x - π/6) is tan(x - π/6).

  2. Step 2: Evaluate the definite integral.

    We need to evaluate tan(x - π/6) from 0 to π/6:

    [tan(x - π/6)]0π/6 = tan(π/6 - π/6) - tan(0 - π/6) = tan(0) - tan(-π/6)

  3. Step 3: Simplify the expression.

    tan(0) = 0 and tan(-π/6) = -tan(π/6) = -1/√3

    Therefore, the result is 0 - (-1/√3) = 1/√3

Correct Answer: 1/√3

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply their knowledge of integration and trigonometric functions to solve a definite integral. They need to recognize the integral of sec^2(x) and then apply the limits of integration.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, namely, evaluating a definite integral using standard integration techniques and applying the fundamental theorem of calculus.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's ability to apply standard integration formulas, a core concept covered in the textbook.

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