Integration of a function

syms x
a = x^6 + 5*x^4 +78
b = diff(a)
c = diff(b)
d = c^2
e = integral(d, x, 0, 3)

Error using integral (line 82)

First input argument must be a function handle.

I am getting this error

Please Help

Answer 1

[John D'Errico]

It can be confusing at times I have seen for newcomers to know which tools apply where, because we have symbolic tools and numerical tools. They often live in subtly different sandboxes.

You know how to differentiate symbolic expressions. That used diff. But you need to understand that integral is a tool for definite NUMERICAL integration. For a symbolic integration, you use int.

syms x
a = x^6 + 5*x^4 +78;
b = diff(a);
c = diff(b);
d = c^2

d = 

e = int(d, x, 0, 3)

e = 

For example, you would use integral to compute a definite integral of a function handle or a function defined in an m-file. For example:

fun = @(x) x.^2 + 2;
integral(fun,1,3)

ans = 12.6667

I could have converted the expression in the variable d, into a function handle. Once it is a function handle, now numerical computations in double precision will apply to it. Then I could have used integral.

dfun = matlabFunction(d)

dfun = function_handle with value:
    @(x)(x.^2.*6.0e+1+x.^4.*3.0e+1).^2

integral(dfun,0,3)

ans = 3.2680e+06

And that should be the same number as e, when expressed as a decimal. Using double, we see:

double(e)

ans = 3.2680e+06

[Jithin D Mathew]

Thanks man