„Analízis (MSc) típusfeladatok” változatai közötti eltérés
| 226. sor: | 226. sor: | ||
<math> u(x, y) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} 1 \cdot \sqrt{\frac{2}{\pi}}\frac{y}{\xi^2 + y^2} d\xi</math> | <math> u(x, y) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} 1 \cdot \sqrt{\frac{2}{\pi}}\frac{y}{\xi^2 + y^2} d\xi</math> | ||
<math> u(x, y) = \frac{y}{\pi} \int_{-\infty}^{\infty} \frac{1}{\xi^2 + y^2} d\xi</math> | |||
<math> u(x, y) = \frac{1}{y \pi} \int_{-\infty}^{\infty} \frac{1}{(\frac{\xi}{y})^2 + 1} d\xi</math> | |||
<math> u(x, y) = \frac{1}{y \pi} \left[arctg \frac{\xi}{y} \right]_{\xi=-\infty}^{\xi=\infty}</math> | |||
<math> u(x, y) = \frac{1}{y \pi} \left( \frac{\pi}{2} - (-\frac{\pi}{2}) \right) = \frac{\pi}{y \pi} = \frac{1}{y}</math> | |||
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