Question Number 91714 by jagoll last updated on 02/May/20
Commented by Tony Lin last updated on 02/May/20
![∫_0 ^2 (ln3^((2π)/3) )e^x^2 dx =(ln3^((2π)/3) )∫_0 ^2 e^x^2 dx =(ln3^((2π)/3) )((√π)/2)[erfi(2)−erf(0)] =(ln3^((2π)/3) )((√π)/2)erfi(2) ≈37.8563](https://www.tinkutara.com/question/Q91743.png)
$$\int_{\mathrm{0}} ^{\mathrm{2}} \left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \right){e}^{{x}^{\mathrm{2}} } {dx} \\ $$$$=\left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \right)\int_{\mathrm{0}} ^{\mathrm{2}} {e}^{{x}^{\mathrm{2}} } {dx} \\ $$$$=\left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \right)\frac{\sqrt{\pi}}{\mathrm{2}}\left[{erfi}\left(\mathrm{2}\right)−{erf}\left(\mathrm{0}\right)\right] \\ $$$$=\left({ln}\mathrm{3}^{\frac{\mathrm{2}\pi}{\mathrm{3}}} \right)\frac{\sqrt{\pi}}{\mathrm{2}}{erfi}\left(\mathrm{2}\right) \\ $$$$\approx\mathrm{37}.\mathrm{8563} \\ $$