JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \( \int_{-\pi/6}^{\pi/6}(\frac{\pi+4x^{11}}{1-\sin(|x|+\pi/6)}) dx \) is equal to:
- A \( 2\pi \)
- B \( 4\pi \)
- C \( 8\pi \)
- D \( 6\pi \)
Answer & Solution
Correct Answer
(B) \( 4\pi \)
Step-by-step Solution
Detailed explanation
\( =2\pi\int_{0}^{\pi/6}\frac{1}{1-\sin(x+\frac{\pi}{6})}dx \) let \( x+\frac{\pi}{6}=t, dx=dt \) \( =2\pi\int_{\pi/6}^{\pi/3}\frac{dt}{1-\sin t}=2\pi\int_{\pi/6}^{\pi/3}\frac{1+\sin t}{\cos^{2}t}dt \)…
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