Question:medium
Let
\[ I(R) = \int_0^R e^{-R \sin x} \, dx, \quad R > 0. \]
Which of the following is correct?
Let
\[ I(R) = \int_0^R e^{-R \sin x} \, dx, \quad R > 0. \]
Which of the following is correct?
\[ I(R) = \int_0^R e^{-R \sin x} \, dx, \quad R > 0. \]
Which of the following is correct?
Show Hint
When dealing with oscillatory integrals, consider numerical techniques or series approximations for better insight into the behavior of the function.
Updated On: Nov 28, 2025
- \(I(R)>\frac{\pi}{2R}(1 - e^{-R})\)
- \(I(R)<\frac{\pi}{2R}(1 - e^{-R})\)
- \(I(R) = \frac{\pi}{2R}(1 - e^{-R})\)
- \(I(R)\) and \(\frac{\pi}{2R}(1 - e^{-R})\) are not comparable
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