Question

i BOX Number- " Parts reference Text CommentsHeader&Footer Links MATLAB Lab 8 This exercise was done previously for a full circle. Perform all the steps shown including the plot, but only for the function shown in part b). Objective: In calculus, integration allows us to find the area under a curve. Numerical methods exist which enable us to approximate the area An interesting approach is to randomly select points in an x-y plane and find the fraction of those points falling below the curve. In these exercises, we will find the area under curves for which y fiox) is a function of x and the values of both x and y are within the range of 0 to 1 Write a MATLAB program (M script file) to implement the steps shown below ng(1791114), Input the number of points (i e. (I) Set the random number seed using trials) (2) Create independent vectors x and y with random values in the range. (3) Find the total number of points below the curve (5) Calculate the approximate area, which is the ratio of number of points below the curve to (6) Plot the points (x and y vectors) and the outline of the curve (you can define X and Y Hint This can be done with a single statement using a logical condition applied vectors y < f(x) combined with the sum function to the total number of points. vectors for that purpose) on the same graph as shown below The curve is the unit circle having the equation (a) (0#x< 1,0<p<1) 0.7854. Note: The area of a quarter circle is π / 4 Run the program for 100 trials and repeat for 1000 trials. Discuss the accuracy of the results (b) Repeat for a sine wave with the equation y = sin (π x) Note: The exact area is 2/π 0.6366.

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clc
clear all
close all
rng(1791114);
n=input('Enter number of points: ');
x=rand(1,n);
y=rand(1,n);
N=sum(y<=sqrt(1-x.^2));
R=N/n;
fprintf('Area is %f\n',R);
plot(x,y,'.',(0:0.01:1),sqrt(1-(0:0.01:1).^2));

MATLAB R2018a Search Documentation Log In EDITOR Run Secton Comparemment%Breakponts Run Pun andAdvance -困Figure 1 Print Indent Eile Edit View Insert lools Desktop wndow Help ÷ ÷ H |L , c.. Users , PRADEEP KALRA Documents MATLAB 、 Current Folder 亙Editor-CNUsers PRADEEPKALRADocumentsMATLAB sa eeem radeep.m × | newton Name 4-rng(1791114) S-n-input('Enter number of points: 6x-rand(,n) 7-y mathlab 0.9 0.8 07 L 0.6 0.5 0.4 RA 0.3 0.2 in rand ,n) R-N/n: fprintf ('Area is %f\n',R); plot (x,y,.., (0:0.01:1),sqrt (1-0:0.01:. New folder 10- a4.m a5.m A1.dat A1.mat A2.dat A3.dat 4.dat AS.det 11- Command Window New to MATLAB? See resources for Getting Started Enter number of points: 10000 Area is 0.781100 Details Name ▲ Value 10000 7811 0.7811 1x10000 double x10000 double 0 0.10. 0.3 04 0.5 0.6 0.7 0.8 0.91 ^徊 11) ENG 11:51 AM IN 05/11/19 O Type here to search

Kindly revert for any queries

Thanks.