WBJEE · Maths · Indefinite Integration
Let \(I(R)=\int_0^R e^{-R \sin x} d x, R\gt0\).
then,
- A \(\quad \mathrm{l}(\mathrm{R})\gt\frac{\pi}{2 \mathrm{R}}\left(1-\mathrm{e}^{-\mathrm{R}}\right)\)
- B \(\quad\) I \((\mathrm{R}) \lt \frac{\pi}{2 R}\left(1-\mathrm{e}^{-\mathrm{R}}\right)\)
- C \(\quad \mathrm{I}(\mathrm{R})=\frac{\pi}{2 \mathrm{R}}\left(1-\mathrm{e}^{-\mathrm{R}}\right)\)
- D I(R) and \(\frac{\pi}{2 R}\left(1-e^{-R}\right)\) are not comparable
Answer & Solution
Correct Answer
(D) I(R) and \(\frac{\pi}{2 R}\left(1-e^{-R}\right)\) are not comparable
Step-by-step Solution
Detailed explanation
Hint : Checking the different positive values of R, can't be comparable.
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