WBJEE · Maths · Definite Integration
Let \(I=\int_{0}^{1} \frac{x^{3} \cos 3 x}{2+x^{2}} d x\). Then
- A \(-\frac{1}{2} < I < \frac{1}{2}\)
- B \(-\frac{1}{3} < I < \frac{1}{3}\)
- C \(-1 < I < 1\)
- D \(-\frac{3}{2} < I < \frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{3} < I < \frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{0}^{1} \frac{x^{3} \cos 3 x}{2+x^{2}} d x\) Here, \(\quad-1 < \cos 3 x < 1\) \(\Rightarrow \quad-x^{3} < x^{3} \cos 3 x < x^{3}\) \(\Rightarrow \quad \frac{-x^{3}}{x^{2}} < \frac{-x^{3}}{x} < \frac{-x^{3}}{2+x^{2}} < \frac{x^{3} \cos 3 x}{2+x^{2}}\)…
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