Question

please use python to do this thx

In this lab you will explore the accuracy of the different quadrature methods. You will explore the Newton-Cotes method using the method of undetermined coefficients. You will also be expected to debug existing code The tutors will provide an explanation (and demonstration) of the Newton-Cotes method using the method of undetermined coefficients. Your task is to implement the Trapezoidal law to approximate the following integral "1 and comment on the accuracy of the method.

Answer 1

The Trapezoidal law represents a method to approximate a given definite integral. It is done by approximation of the area, under the function graph, called trapezoid.

For the given integral:

import numpy as nmpy

import matplotlib.pyplot as plot

%matplotlib inline

f = lambda x: nmpy.exp(-3*x)

x = nmpy.linspace(-0.75,1.5,100)

y = f(x)

plot.plot(x,y)

x0 = -1; x1 = 1;

y0 = f(x0); y1 = f(x1);

plot.fill_between([x0,x1],[y0,y1])

plot.xlim([-0.75,1.5]); plot.ylim([0,1.5]);

plot.show()

This code will show the plot from the approximation of integral. Since number of intervals are not given, accuracy will be affected.