$$

Q$1$

Problem $1$: Numerical Integration

Consider the following function:

$f(x)=e^{-x^2}$

Use Mathematica to numerically integrate $f(x)$ over the range $x=-2$ to $x=$

$2.$ Provide the numerical result and plot the function and its integral. Add plot legend to the graph.

Problem $2$: Particle Motion

A particle is subjected to a constant acceleration a and starts with an initial velocity $v_0$ at $t=0.$ The position of the particle as a function of time is given by:

$x(t)=v_{0}t+0\mathrm{.}5a{t}^2$

Using Mathematica, create a plot of the particle's position for $v_0=5\frac{m}{s}$ and $a=2\frac{m}{s^2}$ over the time interval $0t10$ seconds.