have a question calculating integral

hello guys.

I set up the functions and try to solve the integral but a error has occured.

my code :

syms L;
syms W;
syms a;
syms q;
syms n;
syms m;
syms R;
q = H./L;
a = W./q;
b = (W*(1-R)/(2*q));
m = (0.01*(81.0*W^2 + 180.0*b*W))/a;
n=sqrt(a*m+b^2)-m-b;
syms x;
f=sqrt(a*x+b^2)-x-b;
h=W*0.9-x;
m=(0.01*(80.1*W^2+180.0*b*W)/a);
n=sqrt(a*m+b^2)-m-b;
syms t;
f=@(x) sqrt(a*x+b^2)-x-b;
g=@(x,t) (sqrt(a*t+b^2)-t-b)/t*x;
p=@(x,t) ((sqrt(a*t+b^2)-t-b)-n)/(t-m)*(x-m)+n;
a=integral (f,0,m)-integral (g,0,t)-integral(p,t,m);

and here, I want to calculate the total integral, but some error has occured..

how do I solve it?

thank you.

Answer 1

[Walter Roberson]

You do not define H and you do not declare it symbolic.

You define g and p as function handles of two variables, but you pass them to integral() which expects a function handle of one variable to do a numeric integral of.

You try to integrate f to the upper limit m, but integral() is for numeric integrals and for numeric integrals you need numeric bounds.

Perhaps you want

a = int(f(x),x,0,m) - int(g(x,t),x,0,t) - int(p(x,t),x,t,m);

The result will be a piecewise() expression. It looks to me that is there due to the potential for a division by 0. For example your p(x,t) is undefined if L = 0 and we have no way to know that L is not permitted to be 0.

[Geonhee LEE]

thank you so much!!

and now, I want to input 4 variable (W,H,L,R) and calculate the value of t when a'(t)=0

so below is my code

H=input('input the value of H');

W=input('input the value of W');

L=input('input the value of L');

R=input('input the value of R');

syms H;

syms L;

syms W;

syms a;

syms q;

syms n;

syms m;

syms R;

q = H./L;

a = W./q;

b = (W*(1-R)/(2*q));

m = (0.01*(81.0*W^2 + 180.0*b*W))/a;

n=sqrt(a*m+b^2)-m-b;

syms x;

f=sqrt(a*x+b^2)-x-b;

h=W*0.9-x;

m=(0.01*(80.1*W^2+180.0*b*W)/a);

n=sqrt(a*m+b^2)-m-b;

syms t;

f=@(x) sqrt(a*x+b^2)-x-b;

g=@(x,t) (sqrt(a*t+b^2)-t-b)/t*x;

p=@(x,t) ((sqrt(a*t+b^2)-t-b)-n)/(t-m)*(x-m)+n;

a=integral (f,0,m)-integral (g,0,t)-integral(p,t,m);

solve('derivate(@(t) a)=0');

when I entered this, I put the 4 values

but, the error has occurred...

how do I do after this..?

Thank you so much!!

[Walter Roberson]

After you define H and so on numerically, do not also "syms" those same variable names: doing so is like assigning a new value on top of the numeric value. Just leave them numeric.

You will need to use the int() version I showed, as you are expecting "a" to be a formula rather than a particular numeric result.

Once you have "a" in symbolic form, then

solve(diff(a,t)=0, t)