Class CBSE Class 12 Mathematics Integrals Q #806
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
9. If $\int_{0}^{a}3x^{2}dx=8$, then the value of 'a' is :
(A) 2
(B) 4
(C) 8
(D) 10
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AI Tutor Explanation

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Step-by-Step Solution

  1. Integrate the given function: $\int_{0}^{a}3x^{2}dx = [x^3]_{0}^{a}$
  2. Evaluate the definite integral: $[a^3 - 0^3] = a^3$
  3. Set the result equal to 8: $a^3 = 8$
  4. Solve for 'a': $a = \sqrt[3]{8} = 2$

Correct Answer: 2

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the knowledge of integration to solve the given problem and find the value of 'a'.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (integration and solving for 'a') to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of integration techniques, a core concept covered in the textbook.

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