Question:
Evaluate the integral:
\[
I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx
\]
Evaluate the integral:
\[
I = \int_{\pi/6}^{\pi/3} \cos^{-4} x \, dx
\]
Show Hint
For trigonometric integrals involving negative powers, rewrite in terms of secant or cosecant for easier integration.
Updated On: Jun 5, 2025
- \( \frac{64}{9\sqrt{3}} \)
- \( \frac{52\sqrt{3}}{9} \)
- \( \frac{62\sqrt{3}}{9} \)
- \( \frac{44}{9\sqrt{3}} \)
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The Correct Option is C
Solution and Explanation
Using the identity:
\[
\cos^{-4} x = \sec^4 x
\]
Applying integration methods and simplifying:
\[
I = \frac{62\sqrt{3}}{9}
\]
Thus, the correct answer is:
\[
\frac{62\sqrt{3}}{9}
\]
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