Implement a python function which can numerically integrate a mathematical function. A simple approach based on the Riemann sum is sufficient.

Use it to evaluate the following definite integrals:

$[\backslash$pi $/20]$ arccos$($cosx$/(1+2$cosx $))$dx$.$

$[11]$coshx dx$.$

$[$e $1]1/$xdx$.$

$[10]2$dx$.$

Feel free to use numpy except for functions like np$.$trapz

Report and test your answers, making sure each is accurate to $5$ decimal digits. the exact values are $5/24$ pi $/2,($e$$e$^1),1,$ and $2.$

Additionally, the last integral has to be correct given a small number of discretization steps, say, $1,2,3($using the same function as the others without handling this extra case in a special way$).$ It's essentially meant as a unit test for your algorithm and its implementation. You can use the function provided below.import numpy as np

def constant$\_$function$\_$of$\_$one$($x$)$:

$\text{'}\text{'}\text{'}$Evaluates a constant function returning $1.$

It handles both a single number and np$.$array as input.

Args:

x: either a float or np$.$array of length n

Returns:

either a single $1.($as a float$)$ or a length$-$n np$.$array of $1.$

$\text{'}\text{'}\text{'}$

return $0*$ x $+1$