MATLAB: Derivative after Numerical Integral

numerical differentiationnumerical integration

hello everyone,

I have a function of x, however I get it after calculating a numerical integral, such as:

a = @(x) (integral(@(x1) sqrt((x+4).*(x1+2)./(x1+1)),0,1))

I need to take the derivative of a in terms of x, and then I calculate the values of diff(a) for different x values.

Any help will be appreciated.

Best Answer

Try this:

dfdx = @(f,x) (f(x + 1E-8) - f(x)) ./ 1E-8;                                     % Simple Numeric Derivative
a = @(x) (integral(@(x1) sqrt((x+4).*(x1+2)./(x1+1)),0,1, 'ArrayValued',1))
x = linspace(-1, 1, 25);
dadx = dfdx(a,x);
figure
plot(x, dadx)
grid

Make appropriate changes to ‘x’ for your needs.

EDIT —

You can also use the gradient (link) function to calculate the derivative of a (regularly-spaced) vector of values proeuced by your ‘a’ function.

Related Solutions

MATLAB: Numerical integration Matlab plot

You can do it using arrayfun (similar to for-loop, but compact)

x1 = logspace(-9, -6, 10);
fun = @(x) (1./(exp(0.00004781./(x))-1).*1./x.^4);
y = arrayfun(@(x1_) integral(fun, 0, x1_), x1);
semilogx(x1, int_fun);

MATLAB: How to find a limit without syms and limit function

Crude but effective (for this function, may not be universally applicable):

fcn = @(x) (x.^3 - 1) ./ (x - 1);
x = 1;
lm = fcn(x-1E-15)
lm =
     3

Experiment to get the result you want.

EDIT —

Another option is to use a simple numerical derivative:

dfdx = @(f,x) (f(x + 1E-8) - f(x)) ./ 1E-8;
fcnn = @(x) x.^3 - 1;
fcnd = @(x) x - 1;
xv = 1;
Lm = dfdx(fcnn,xv) ./ dfdx(fcnd,xv)

producing:

Lm =
3

Best Answer

Related Solutions

MATLAB: Numerical integration Matlab plot

MATLAB: How to find a limit without syms and limit function

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