i need to make integrat for this equation from 0 to x ,, with respect to x ,,i make several program but i cant reach to my object

y= sqrt(2*m*(E-(a.*x)))

where m,E,A, IS constant

[Stephan]

Do you want to solve numeric or analytical?

[Aalaa Abu alrob]

analyticaly

Answer 1

[Stephan]

Hi,

syms g(x) a m E 
g(x) = (sqrt(2*m*(E-(a.*x))))
G(x) = int(g(x),x)
pretty(G(x))

gives the indefinite integral, which is:

G(x) =

-(2*2^(1/2)*(m*(E - a*x))^(1/2)*(E - a*x))/(3*a)

or by using pretty:

    2 sqrt(2) sqrt(m (E - a x)) (E - a x)
  - -------------------------------------
                     3 a

Best regards

Stephan

[Aalaa Abu alrob]

Thanks for your attention Yes .. thats what i want But i need the untegrate from o to x what about zero !! How i can make it ..!!

[Stephan]

Like we learned this once in our math classes:

1. Get the indefinite integral function G(x) --> Check

2. substitute the upper and lower limits of integration and subtract. --> To Do

[Torsten]

Should be G(x)-G(0), shouldn't it ?

[Stephan]

I think so

[Aalaa Abu alrob]

Thank very much I try it .. but has you an opinion how to collect term (add..subtract ..) And the term i get too long .. Such a code !!

[Stephan]

fun_x1 = G(x);
fun_x0 = G(0);
result = simplify(fun_x1 - fun_x0);
pretty(result)

gives:

2 sqrt(2) E sqrt(E m)   2 sqrt(2) sqrt(m (E - a x)) (E - a x)
--------------------- - -------------------------------------
         3 a                             3 a

which is the analytical solution of your integral in the bounds from 0...x. To calculate values for this use:

fun = matlabFunction(result)

which is:

fun =

    function_handle with value:

      @(E,a,m,x)(sqrt(2.0).*E.*sqrt(E.*m).*(2.0./3.0))./a-(sqrt(2.0).*sqrt(m.*(E-a.*x)).*(E-a.*x).*(2.0./3.0))./a

This function handle you can call like shown in this example:

m = 10;
E = 2;
a =  0.3;
x = 5
numeric_result = fun(E,a,m,x)

and ist value is:

numeric_result =

     24.5955