JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} d x=\frac{1}{a} \log _e\left(\frac{a}{3}\right)+\frac{\pi}{b \sqrt{3}}\), where a, \(\mathrm{b} \in \mathrm{N}\), then \(\mathrm{a}+\mathrm{b}\) is equal to ...........
- A \(6\)
- B \(8\)
- C \(4\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(8\)
Step-by-step Solution
Detailed explanation
\( \int_0^{\frac{\pi}{2}} \frac{\sin ^2 x}{1+\frac{1}{2} \sin 2 x} d x=\int_0^{\frac{\pi}{4}} \frac{1-\cos 2 x}{2+\sin 2 x} d x \) \( \int \frac{1}{2+\sin 2 x}-\int \frac{\cos 2 x}{2+\sin 2 x}\) \( \left.\left(\mathrm{I}_1\right)-\mathrm{I}_2\right) \)…
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