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AP EAMCET · Maths · Definite Integration

\(\int_0^{3 \pi / 2} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x=\)

  1. A \(0\)
  2. B \(1\)
  3. C \(\frac{\pi}{4}\)
  4. D \(\frac{3 \pi}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3 \pi}{4}\)

Step-by-step Solution

Detailed explanation

\( I = \int_0^{3 \pi / 2} \frac{\cos^3 x}{\cos^3 x+\sin^3 x} dx \) \( I = \int_0^{3 \pi / 2} \frac{\cos^3 (3 \pi / 2 - x)}{\cos^3 (3 \pi / 2 - x)+\sin^3 (3 \pi / 2 - x)} dx \) \( I = \int_0^{3 \pi / 2} \frac{(-\sin x)^3}{(-\sin x)^3+(-\cos x)^3} dx \)…