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AP EAMCET · Maths · Definite Integration

\(\int_0^{\pi / 4} \frac{d x}{\cos ^3(x) \cdot \sqrt{2 \sin (2 x)}}=\)

  1. A \(\frac{6}{5}\)
  2. B \(\frac{3}{5}\)
  3. C \(\frac{4}{5}\)
  4. D \(\frac{8}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{6}{5}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} I & =\int_0^{\pi / 4} \frac{d x}{\cos ^3 x \sqrt{2 \sin 2 x}}=\int_0^{\pi / 4} \frac{d x}{\cos ^3 x \sqrt{4 \sin x \cos x}} \\ & =\int_0^{\pi / 4} \frac{d x}{2 \cos ^4 x \sqrt{\tan x}}=\frac{1}{2} \int_0^{\pi / 4} \frac{\sec ^2 x\left(1+\tan ^2…