WBJEE · Maths · Definite Integration
If \(\mathrm{I}\) is the greatest of \(I_1=\int_0^1 e^{-x} \cos ^2 x d x, I_2=\int_0^1 e^{-x^2} \cos ^2 x d x, I_3=\int_0^1 e^{-x^2} d x, I_4=\int_0^1 e^{-x^2 / 2} d x\), then
- A \(\mathrm{I}=\mathrm{I}_1\)
- B \(\mathrm{I}=\mathrm{I}_2\)
- C \(I=I_3\)
- D \(\mathrm{I}=\mathrm{I}_4\)
Answer & Solution
Correct Answer
(D) \(\mathrm{I}=\mathrm{I}_4\)
Step-by-step Solution
Detailed explanation
\(\mathrm{e}^{-\mathrm{x}} \cdot \cos ^2 \mathrm{x} < \mathrm{e}^{-\mathrm{x}^2} \cos ^2 \mathrm{x} < \mathrm{e}^{-\mathrm{x}^2} < \mathrm{e}^{-\frac{\mathrm{x}^2}{2}}\) for \(0 < \mathrm{x} < 1\) \(\therefore\) By domination Law, \(\mathrm{I}_4\) is maximum…
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