AP EAMCET · Maths · Definite Integration
\(\int_{\pi / 6}^{\pi / 3} \cos ^{-4} x d x=\)
- A \(\frac{64}{9 \sqrt{3}}\)
- B \(\frac{52 \sqrt{3}}{9}\)
- C \(\frac{62 \sqrt{3}}{9}\)
- D \(\frac{44}{9 \sqrt{3}}\)
Answer & Solution
Correct Answer
(D) \(\frac{44}{9 \sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\( \int_{\pi / 6}^{\pi / 3} \cos ^{-4} x d x = \int_{\pi / 6}^{\pi / 3} \sec^4 x d x \) \( = \int_{\pi / 6}^{\pi / 3} \sec^2 x (1 + \tan^2 x) d x \) \( = [\tan x + \frac{\tan^3 x}{3}]_{\pi / 6}^{\pi / 3} \)…
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