Need help with the coding in python.

Important note:

This is supposed to be a short homework. The solution key has a total of $15$ lines$/$commands$.$

Question:

$x(f)$ is defined as

$x(f)=\{\begin{array}{ccc}(1-f^2{)}^{\frac{1}{4}}& if& -1f1\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

The plot shown on the left is $|x(f)|$ versus $f.$

If we plot $|x(f){|}^2,$ we get the half circle shown on the right. The area under $|x(f){|}^2$ will be the energy of the signal, $x(t).$ Note that this area is $\frac{}{2},$ hence the signal must have energy equal to $\frac{}{2}.$

$[]$ # COMMANDS USED TO GENERATE THESE PLOTS ARE DELETED

# COMMANDS USED TO GENERATE THESE PLOTS ARE DELETED

$(1)$ Compute the inverse Fourier transform integral

$x(t)={\displaystyle \underset{-}{\overset{}{}}}x(f)e^{j2ft}df$

numerically, and plot $x(t)$ versus $t.$

$(2)$ Then compute the integral

${\displaystyle \underset{-}{\overset{}{}}}|x(t){|}^{2}dt$

numerically, and verify that it is indeed equal to $\frac{}{2}.$

# I USED TOTAL $11$ LINES$/$COMMANDS TO COMPUTE THE INTEGRAL AND PLOT

$[]$ # I USED TOTAL $4$ LINES$/$COMMANDS FOR THE INTEGRAL

Energy integral computed numerically $=1\mathrm{.}5701513734782635$ Value of pi$/2,=1\mathrm{.}5707963267948966$