JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \( I=\int_{\frac{\pi}{24}}^{\frac{5\pi}{24}}\frac{dx}{1+\sqrt[3]{\tan 2x}} \) is:
- A \( \frac{\pi}{12} \)
- B \( \frac{\pi}{18} \)
- C \( \frac{\pi}{6} \)
- D \( \frac{\pi}{3} \)
Answer & Solution
Correct Answer
(A) \( \frac{\pi}{12} \)
Step-by-step Solution
Detailed explanation
\(I=\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{d x}{1+\sqrt[3]{\tan 2 x}}\) ...(1) Apply king \(I=\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{d x}{1+\sqrt[3]{\tan 2\left(\frac{\pi}{4}-x\right)}}\)…
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