Chapter 8.3, Problem 16ES

(a) Show that the solution of the initial-value problem

$y^{\prime }=e^{-x^2},y\left(0\right)=0\text{ is }y\left(x\right)={\displaystyle {\int }_0^x{e}^{-t}{}^{{}^2}}dt$

(b) Use Euler's Method with $\Delta x=0.05$ to approximate the value of

$y\left(1\right)={\displaystyle {\int }_0^1{e}^{-t}{}^{{}^2}}dt$

and compare the answer to that produced by a calculating utility with a numerical integration capability.