Class CBSE Class 12 Mathematics Integrals Q #801
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
∫ [sec x / (sec x - tan x)] dx equals
(A) sec x - tan x + c
(B) sec x + tan x + c
(C) tan x - sec x + c
(D) -(sec x + tan x) + c
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AI Tutor Explanation

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Step-by-Step Solution

Let I = ∫ [sec x / (sec x - tan x)] dx

Multiply numerator and denominator by (sec x + tan x):

I = ∫ [sec x (sec x + tan x) / (sec2 x - tan2 x)] dx

Since sec2 x - tan2 x = 1:

I = ∫ (sec2 x + sec x tan x) dx

Integrate each term separately:

I = ∫ sec2 x dx + ∫ sec x tan x dx

We know that ∫ sec2 x dx = tan x + c1 and ∫ sec x tan x dx = sec x + c2

Therefore, I = tan x + sec x + c, where c = c1 + c2

Correct Answer: sec x + tan x + c

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the rules of integration and trigonometric identities to solve the problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure of algebraic manipulation and integration techniques 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 knowledge of integration techniques and trigonometric identities as covered in the textbook.

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