Question

Write a user-defined function, in MATLAB, with function call val=evalf(f,a,b) where f is an inline function, and a and b are constants such that a<b. The function calculates the midpoint m of the interval [a,b] and returns the value of (1/2)f(a)+(1/3)f(m)+(1/4)f(b). Execute the function for f(x)=e^(-x)*cos(2x), a=-1, b=3.

Answer 1

//Screenshot of the code:

//evalf.m

//main.m

//Sample Output:

//Code to copy:

//evalf.m

%Define a function evalf to evaluate the function f(x) = %e^(-x)*xos(2*x).

function value = evalf(f,a,b)

%Find the mid point of the a and b.

m = (a+b)/2;

%Calculate the value of the variable val. Function f is an %inline function and replace f(a), f(b), and f(m) with the %expression exp(-a)*cos(2*a), exp(-b)*cos(2*b), and %exp(-%mid)*cos(2*m).

value = (1/2).*f(a)+(1/3).*f(m)+(1/4).*f(b);

%End the function.

end

//main.m

%Make a function f(x) = e^-x*cos(2*x) inline.

f =inline('exp(-x).*cos(2*x)');

%Call the function evalf and pass the inline function, -1, %and 3 as arguments.

val = evalf(f,-1,3)