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Match the integrals in Column I with the corresponding functions in Column II. Column I: A. \(\int \sec x\tan x\,dx\) B. \(\int \cosec x\cot x\,dx\) C. \(\int \cosec^2 x\,dx\) D. \(\int \cos x\,dx\) Column II: (p) \(-\cosec x + C\) (q) \(-\cot x + C\) (r) \(\sec x + C\) (s) \(\sin x + C\)

1. A–(p), B–(q), C–(r), D–(s)
2. A–(q), B–(p), C–(r), D–(s)
3. A–(r), B–(p), C–(q), D–(s)
4. A–(p), B–(r), C–(q), D–(s)

Correct answer: A–(r), B–(p), C–(q), D–(s)

Solution

Using standard results: \(\int \sec x\tan x\,dx=\sec x+C\), \(\int \cosec x\cot x\,dx=-\cosec x+C\), \(\int \cosec^2 x\,dx=-\cot x+C\), and \(\int \cos x\,dx=\sin x+C\). Therefore the correct matching is A–(r), B–(p), C–(q), D–(s).

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