JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int \limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x\) is equal to
- A \(\frac{7}{2}-\sqrt{3}-\log _e \sqrt{3}\)
- B \(-2+3 \sqrt{3}+\log _e \sqrt{3}\)
- C \(\frac{10}{3}-\sqrt{3}+\log _e \sqrt{3}\)
- D \(\frac{10}{3}-\sqrt{3}-\log _e \sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{10}{3}-\sqrt{3}+\log _e \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(\int \limits_{\pi / 3}^{\pi / 2}\left(\frac{2+3 \sin x}{\sin x(1+\cos x)}\right) d x=2 \int \limits_{\pi / 3}^{\pi / 2} \frac{d x}{\sin x+\sin x \cos x}+3\) \(3 \int \limits_{\pi / 3}^{\pi / 2} \frac{d x}{1+\cos x}\)…
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