How to define the function to use for the composite trapezoidal rule?

Im trying to define the function to be integrated possibly in a sub-function, but I cant seem to do it without it saying INVALID.

My work is below.

Thanks

clc

clear

%intial conditions

t=linspace(1,10,10);

v=zeros(size(t));

m=1609.344/3600;%conversion from mph to m/s

for i=1:numel(t)

v(i)=((0.0011*(t(i)^6))-(0.02928*(t(i)^05))+(0.2807*(t(i)^4))-(1.1837*(t(i)^3))-(0.8283*(t(i)^2))+(41.234*(t(i))-3.3549))*m;

hold on

end

plot(t,v,'r*-')

title('9 Seconds of Car Driving-Speed(m/s)vs.Time(s)')

xlabel('Time(s)')

ylabel('Speed(m/S)')

a=1; %lower limit

b=10; %upper limit

n=9; %number of sub-intervals

r_error=0.1;%intial realtive error

i=0; %loop counter

I=0; %integral set to zero

%while loop to find new integral with a realtive error less than 0.0002%

while r_error>0.00002

h=(b-a)/n; %distnace of each separation

new_i=0; %intially set to zero

i=i+1; %increase counter by 1 every loop

for m=1:n

x_left=a+(i-1)*h;

x_right=a+(i*h);

f_left=f(x_left);

f_right=f(x_right);

new_i=(h/2)*(f_left+f_right)+I; %new integral

New_x=new_i; %new distance is equal to new integral

midpoint=(a+b)/2;

end

r_error=((new_i-I)/new_i)*100; %realtive error

n1(i)=n;

New_x=new_i;

n=n*2; %number of separtions doubled every loop

I=new_i; %new integral is stores as old integral for new loop

fprintf('Integral=%6.3f\n',I) %new integral value displayed to 3 decimal places

fprintf('Number of separations=%6.0f\n',n) % displaying number of separations

fprintf('Relative Error=%6.5f\n',r_error) %displaying relative error to 5 decimal places

end

function v=f(t)

v=((0.0011*t^6)-(0.02928*t^5)+(0.2807*t^4)-(1.1837*t^3)-(0.8283*t^2)+(41.243*t)-3.3549);

end

Answer 1

[KALYAN ACHARJYA]

"but I cant seem to do it without it saying INVALID."

I did not find any coding error

Main Script:

%intial conditions 
t=linspace(1,10,10);
v=zeros(size(t));
m=1609.344/3600;%conversion from mph to m/s
for i=1:numel(t)
v(i)=((0.0011*(t(i)^6))-(0.02928*(t(i)^05))+(0.2807*(t(i)^4))-(1.1837*(t(i)^3))-(0.8283*(t(i)^2))+(41.234*(t(i))-3.3549))*m;
hold on
end
plot(t,v,'r*-')
title('9 Seconds of Car Driving-Speed(m/s)vs.Time(s)')
xlabel('Time(s)')
ylabel('Speed(m/S)')
a=1; %lower limit
b=10; %upper limit
n=9; %number of sub-intervals 
r_error=0.1;%intial realtive error
i=0; %loop counter
I=0; %integral set to zero
%while loop to find new integral with a realtive error less than 0.0002%
while r_error>0.00002
    h=(b-a)/n; %distnace of each separation
    new_i=0; %intially set to zero
    i=i+1; %increase counter by 1 every loop
    for m=1:n
        x_left=a+(i-1)*h;
        x_right=a+(i*h);
        f_left=f(x_left);
        f_right=f(x_right);
        new_i=(h/2)*(f_left+f_right)+I; %new integral 
        New_x=new_i; %new distance is equal to new integral 
        midpoint=(a+b)/2; 
    end
    r_error=((new_i-I)/new_i)*100; %realtive error
    n1(i)=n;
    New_x=new_i;
    n=n*2; %number of separtions doubled every loop
    I=new_i; %new integral is stores as old integral for new loop
    fprintf('Integral=%6.3f\n',I) %new integral value displayed to 3 decimal places 
    fprintf('Number of separations=%6.0f\n',n) % displaying number of separations
    fprintf('Relative Error=%6.5f\n',r_error) %displaying relative error to 5 decimal places
end

Function f (save in same directory)

function v=f(t)
v=((0.0011*t^6)-(0.02928*t^5)+(0.2807*t^4)-(1.1837*t^3)-(0.8283*t^2)+(41.243*t)-3.3549);
end

Results:

Integral=53.051
Number of separations=    18
Relative Error=100.00000
Integral=84.010
Number of separations=    36
Relative Error=36.85149
Integral=98.508
Number of separations=    72
Relative Error=14.71783
Integral=104.973
Number of separations=   144
Relative Error=6.15875
Integral=107.866
Number of separations=   288
Relative Error=2.68245
Integral=109.191
Number of separations=   576
Relative Error=1.21350
Integral=109.814
Number of separations=  1152
Relative Error=0.56711
Integral=110.113
Number of separations=  2304
Relative Error=0.27165
Integral=110.259
Number of separations=  4608
Relative Error=0.13234
Integral=110.331
Number of separations=  9216
Relative Error=0.06517
Integral=110.367
Number of separations= 18432
Relative Error=0.03230
Integral=110.384
Number of separations= 36864
Relative Error=0.01607
Integral=110.393
Number of separations= 73728
Relative Error=0.00802
Integral=110.398
Number of separations=147456
Relative Error=0.00400
Integral=110.400
Number of separations=294912
Relative Error=0.00200
Integral=110.401
Number of separations=589824
Relative Error=0.00100
Integral=110.401
Number of separations=1179648
Relative Error=0.00050
Integral=110.402
Number of separations=2359296
Relative Error=0.00025
Integral=110.402
Number of separations=4718592
Relative Error=0.00012
Integral=110.402
Number of separations=9437184
Relative Error=0.00006
Integral=110.402
Number of separations=18874368
Relative Error=0.00003
Integral=110.402
Number of separations=37748736
Relative Error=0.00002
>> 

[james carsley]

The integral produced is the integral of speed,v(mph) so the integral is not in meters like the graph. For the graph I multiplied v by the conversion rate to get m/s, but if in attempt this in the function for the integral it doesnt work. How would I achieve the integral to be in meters?

The integral needed is around 480m.

Answer 2

[james carsley]

Thank you very much!