Question

5. Basic integration TV2 Show that tan 1 = (sin? x dx = SV1- x? dx. 0 6. Integration with simple probability application The results x of a certain biological test are found to be normally distributed, with an average value u of 800 and a standard deviation o of 100. We can define zo = (x – u)/o as a measure of the number of standard deviations from the mean that a number x is. It can be shown that the probability that a test score will be above a certain value xo is given by p(x 2 xo) = 1 / 15 Se 2²/2d2 "dz. Find and print the probability that x will be a value the user enters. First, use the int function (and vpa) and then use the integral function. Three sample runs are shown below. >> HW10 06 Find the probability that x will be greater than what? 600 Definite Integral: probability that x > 600.000000 is 97.724987%. Numerical Integral: probability that x > 600.000000 is 97.724987%. >> HW10 06 Find the probability that x will be greater than what? 900 Definite Integral: probability that x > 900.000000 is 15.865525%. Numerical Integral: probability that x > 900.000000 is 15.865525%. >> HW10 06 Find the probability that x will be greater than what? 800 Definite Integral: probability that x > 800.000000 is 50.000000%. Numerical Integral: probability that x > 800.000000 is 50.0000008.

Using MATLAB, please solve questions 5 and 6.

Answer 1

clc
clear all
close all
format long
disp('tan(1)^-1=')
atan(1)
disp('sin(x)^2 integration=');
f=@(x) sin(x).^2;
integral(f,0,pi/2)
disp('sqrt(1-x^2) integration=');
f=@(x) sqrt(1-x.^2);
integral(f,0,1)
disp('Since all 3 are equal so the statement is true')