Calculate the area between two curves

i need help! i am new at using the Matlab and Scilab softwares and i need to calculate the area between the curves y=f(x) and y=g(x) in the interval [a,b] with a = 3, b = 6,

f (x)=sin(3 x+1) and g(x)=(e∣x∣/2−2−1)

by means of the composite trapezoidal rule with 73 trapezoids,Recall that the area between f and g in [a,b] is

b a ∫ ∣f(x)−g(x)∣dx

The approximate value of the area has to be displayed at the end, and the script must contain all the code to obtain the result.

how do i even begin with this? any help is much appreciated. thanks

Answer 1

[Alberto]

f =@(x) sin(3.*x+1) ;

g=@(x) exp(abs(x)/2 -2)-1;

a=3; b=6;

x=linspace(a,b,73); S=0;

for k=1:length(x)-1

S=S+abs( f(x(k+1)) - g(x(k+1)) - f(x(k)) +g(x(k)) )/2;

end

S

[maria]

thank you! thank you!!! i have tried this out on my pc.. and i get S = 0 for all 72 columns. is this it for that question or is there another step afterwards and i have uploaded an image that came with the question. please take a look at it.. i know i am hopeless but bear with me for a bit longer..

[Alberto]

Actually S is not a vector; S has the cumulative sum of trapezoids. The value I get is:

S = 2.7752

and has no columns. Maybe there are some conflicts with other parts.

Show me your whole code so I can check