MATLAB: I keep getting ‘Index exceeds array bounds.’ the code doesn’t like r(i)

array boundserrorerror message

%function [int_ft] = gerberdolan_jessica_hw09_int(t, f)
%INPUT:
%t = vector of t values at which the function is provided
%f = vector of values of the function at the points contained in t
%OUTPUT:
%int_ft = value of integral
%start this function as a script with the following test senario
t = [0 pi/4 pi/2 3*pi/4 pi]
f = cos(t)+5
for i = 1:(length(t)-1)
t = t(i);
r(i) = f(i).*(t(i+1)-t(i))
%((t(1+1)-t(i)) is delta x
%f(t(i)) is the base rantagle for the retangular rule
%r is rectangle
tr(i) = (f(t(i))-f(t(i+1)))*(t(1+1)-t(i))*1/2
%tr is the triangle on top
%(f(t(i))-f(t(i+1))) is the height difference
%(t(1+1)-t(i)) is delta x
%1/2 is to make it a triangle
a_of_trap(i) = r(i) + tr(i)
%area of trapizoid is the rectangle plus the triangle
end
int_ft = sum(a_of_trap)

Best Answer

Initially in your code, t is a vector. 
t = [0 pi/4 pi/2 3*pi/4 pi]
t =
            0       0.7854       1.5708       2.3562       3.1416
Then within your i loop, you overwrite t as a scalar. 
t = t(i)
t =
     0
Immediately after this, you try to grab the 2nd element of t even though t now only has 1 element. This is why the index (i+1) exceed array bounds. Because at this point, t is only 1 element long. 
     r(i) = f(i).*(t(i+1)-t(i))
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