SOLVE IN PYTHON!

f$($x$)=$ x$^$cos$($x$^2),$ integral from $0$ to $4($f$($x$)$dx$)$

Recall the left endpoint rule $($example illustrated below$)$:

${\displaystyle \underset{a}{\overset{b}{}}}g(x)dx$~~${\displaystyle \underset{i=1}{\overset{n}{}}}g(x_{i-1})x$

where $x_i=a+i*x$ and $x=\frac{1}{n}(b-a).$

Follow the steps below. Only parts $($c$)$ and $($d$)$ require

printed output in your submitted work.

$($a$)$ Define a Python function that accepts an ordered pair $($representing an interval$)$ as its input and returns the numerical result of applying the left endpoint rule to f$($x$)$ on that interval.

$($b$)$ Use the function you wrote in part $($a$)$ to define a new Python list that contains the results of applying the left endpoint rule to f$($x$)$ on each subinterval in Partition.

$($c$)$ Sum the list from part $($b$)$ to obtain an approximation for the area under f$($x$)$ on $[0,4].$Print your output without rounding. The result should be $4\mathrm{.}03535533686618$ if you have set up your approximation correctly.

$($d$)$ The true value of integral from $0$ to $4($f$($x$)$dx$)$ to $15$ decimal places is $4\mathrm{.}046085774496901.$ Use this value to print an estimate for the error $=|$actual $$ approximation$|.$