WBJEE · Maths · Definite Integration
Let \(\mathrm{I}=\int_{\pi / 4}^{\pi / 3} \frac{\sin \mathrm{x}}{\mathrm{x}} \mathrm{dx}\). Then
- A \(\frac{\sqrt{3}}{8} \leq \mathrm{I} \leq \frac{\sqrt{2}}{6}\)
- B \(\frac{\sqrt{3}}{2 \pi} \leq \mathrm{I} \leq \frac{2 \sqrt{3}}{\pi}\)
- C \(\frac{\sqrt{3}}{9} \leq \mathrm{I} \leq \frac{\sqrt{2}}{16}\)
- D \(\pi \leq \mathrm{I} \leq \frac{4 \pi}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{3}}{8} \leq \mathrm{I} \leq \frac{\sqrt{2}}{6}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{\sin x}{x}\) (decreasing function) \(\Rightarrow f\left(\frac{\pi}{3}\right) < f(x) < f\left(\frac{\pi}{4}\right)\)…
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