Question:
Evaluate the integral with square root in denominator.
\[ \int \frac{\sin 2x \cos 2x}{\sqrt{9-\cos^4 2x}}\,dx \]
Evaluate the integral with square root in denominator.
\[ \int \frac{\sin 2x \cos 2x}{\sqrt{9-\cos^4 2x}}\,dx \]
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For any integration question, always check that the full integral is present:
• integrand,
• variable,
• limits if definite. e} If the actual integral is missing, the answer cannot be found uniquely.
• integrand,
• variable,
• limits if definite. e} If the actual integral is missing, the answer cannot be found uniquely.
Updated On: May 14, 2026
- \(\frac{1}{4} \sin^{-1}\left(\frac{\cos^2 2x}{2}\right)\)
- \(\frac{-1}{4} \sin^{-1}\left(\frac{\cos^2 2x}{2}\right)\)
- \(\frac{1}{2} \sin^{-1}\left(\frac{\cos^2 2x}{2}\right)\)
- \(\frac{-1}{2} \sin^{-1}\left(\frac{\cos^2 2x}{2}\right)\)
- None of these
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The Correct Option is
Solution and Explanation
To evaluate an integral, the complete integral expression is necessary.
A complete integral question must contain:
• the integrand,
• the variable of integration,
• and, if it is definite, the limits of integration. e} In this question, only the answer options are visible, while the actual integral is missing. So the proper solving steps cannot be started because:
• we do not know what function is present in the numerator,
• we do not know the exact square root expression in the denominator,
• we do not know whether the integral is indefinite or definite,
• and we cannot verify which option matches the antiderivative. e} Normally, if the integral had been given, we would:
• first simplify the expression inside the square root,
• then use a suitable substitution,
• then integrate carefully,
• and finally compare the result with the given options. e} Since the actual integral is absent, none of these steps can be carried out. Hence, the correct option cannot be determined reliably from the available content.
• the integrand,
• the variable of integration,
• and, if it is definite, the limits of integration. e} In this question, only the answer options are visible, while the actual integral is missing. So the proper solving steps cannot be started because:
• we do not know what function is present in the numerator,
• we do not know the exact square root expression in the denominator,
• we do not know whether the integral is indefinite or definite,
• and we cannot verify which option matches the antiderivative. e} Normally, if the integral had been given, we would:
• first simplify the expression inside the square root,
• then use a suitable substitution,
• then integrate carefully,
• and finally compare the result with the given options. e} Since the actual integral is absent, none of these steps can be carried out. Hence, the correct option cannot be determined reliably from the available content.
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