find the arc length of the curve formed by the function f(x)=13x.^2+23/2 on the interval from x=0 to x=4 in matlab

To find the arc length of the curve in MATLAB, we can use the formula:

main.m
arc_length = integral(@(x) sqrt(1 + (diff(f(x)).^2)), 0, 4);
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This uses the integral function in MATLAB to numerically evaluate the integral of the square root of one plus the squared derivative of the function f with respect to x. The interval of integration is from 0 to 4, as specified in the question.

Here's the complete code:

main.m
f = @(x) 13 .* x.^2 + 23/2;

arc_length = integral(@(x) sqrt(1 + (diff(f(x)).^2)), 0, 4);

disp(arc_length);
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This will output the arc length of the curve formed by the function f(x) on the interval from x=0 to x=4.