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Question Number 207801 by naka3546 last updated on 27/May/24

$$\underset{t\to \mathrm{\infty }}{\lim }\underset{0}{\stackrel{\pi }{\int }}\frac{\sin \left(\mathrm{t}x\right)}{x}dx=\cdot \cdot \cdot$$

Commented by naka3546 last updated on 27/May/24

$$t\to \mathrm{\infty }$$

Answered by Frix last updated on 27/May/24

$$\underset{0}{\stackrel{\pi }{\int }}\frac{\sin tx}{x}dx=\mathrm{Si}\pi t$$$$\underset{n\to \mathrm{\infty }}{\lim }\mathrm{Si}n=\frac{\pi }{2}$$

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