Question:
Evaluate the integral:
\[
I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx
\]
Evaluate the integral:
\[
I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx
\]
Show Hint
For definite integrals involving trigonometric functions, check for symmetry in the interval to simplify evaluation.
Updated On: Jun 5, 2025
- \( 0 \)
- \( 1 \)
- \( \frac{\pi}{4} \)
- \( \frac{3\pi}{4} \)
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The Correct Option is A
Solution and Explanation
Using symmetry properties of trigonometric functions:
\[
I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx
\]
Splitting the integral into symmetric regions and simplifying,
\[
I = 0
\]
Thus, the correct answer is:
\[
0
\]
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