3. Write a function TrapezoidalRule.m which takes three input arguments f, a and b and returns one output argument I. You must use a for loop to compute the trapezoidal rule approximation to the integral 1 = = b-a N-1 Use the definition line function [I] = The input arguments mus where h = N-1 +fN [ f(x)dx = n(f₁ + fx + [fu) h 2 k=2 zoidalRule(f,a,b) 1 x N array f scalar (1 x 1 array) a and b scalar (1 x 1 array) I Test your function with f= [0:0.1:2].^3, a-0, b-2 which should give I = 4.01000. must be auffal The output argument must be

(Useful utility) Modify the program written for Exercise 3 to search for the first occurrence of a user-entered sequence of characters, and then replace this sequence, when it’s found in the string, with a second user-entered sequence. For example, if the entered string is Figure 4-4 illustrates the output of Program 4-2 and the user enters that 4- is to be replaced by 3-, the resulting string is Figure 3-4 illustrates the output of Program 4-2. (Only the first occurrence of the searched-for sequence has been changed.)

(Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.

(Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.

Write a program that takes as input five numbers and outputs the mean (average) and standard deviation of the numbers. If the numbers are x1,x2,x3,x4,andx5, then the mean is x=(x1+x2+x3+x4+x5)/5 and the standard deviation is: s=(x1x)2+(x2x)2+(x3x)2+(x4x2)+(x5x2)5 Your program must contain at least the following functions: a function that calculates and returns the mean and a function that calculates the standard deviation.

Write a program that reads in a line consisting of a students name, Social Security number, user ID, and password. The program outputs the string in which all the digits of the Social Security number and all the characters in the password are replaced by x. (The Social Security number is in the form 000-00-0000, and the user ID and the password do not contain any spaces.) Your program should not use the operator [] to access a string element. Use the appropriate functions described in Table 7-1.