It can be shown that the solution to the initial value problem $$y'=e^{-\left(\frac{x}{5}\right)^{2}}, y(1)=0$$ is $$y(x)=\displaystyle \int_{1}^{x} e^{-\left(\frac{t}{5}\right)^{2}}\; dt$$

Use Euler's Method with $\Delta x=0.1$ to approximate $y(3)=\displaystyle \int_{1}^{3} e^{-\left(\frac{t}{5}\right)^{2}}\; dt$ to six decimal places (do not round intermediate results).

$y(3)\approx$