Evaluating the area between two curves.

how to Evaluate the area between two curves using matlab? for example this one y=x^2 and y=2*x

[kalash vasaniya]

Find the area of the region bounded by the curves x=y^3 and x=y^2 in matlab

[Walter Roberson]

syms x y
fimplicit([x == y^3, x == y^2], [-1 10])

@kalash vasaniya

Which of the two areas? The right-hand one is obviously unbounded, but your instructions do not say to do only the other area.

And please explain how your instructions will solve the question asked 10 years ago by Ejay Kasai ??

Answer 1

[Grzegorz Knor]

http://www.mathworks.com/matlabcentral/answers/15551-how-to-compute-for-the-points-of-intersection-of-2-curves

http://www.mathworks.com/matlabcentral/answers/15550-how-to-create-a-matlab-program-computing-area-between-2-curves

In your case:

syms x
x0 = eval(solve('x^2 -2*x'));

x = linspace(x0(1),x0(2),100);
y1 = x.^2;
y2 = 2*x;

fill([x x(end:-1:1)],[y1 y2(end:-1:1)],'r')
hold on
plot(x,y1,x,y2,'LineWidth',2)
grid on
a = trapz(x,y2)-trapz(x,y1);

Instead of:

syms x
x0 = eval(solve('x^2 -2*x'));

You can use:

x0(1) = fzero('x.^2 -2*x',1);
x0(2) = fzero('x.^2 -2*x',1.5);

[Ejay Kasai]

i mean determining the value not by shading.

[Oleg Komarov]

So, you're not happy with "a"?

[Ejay Kasai]

what do you mean i'm not happy with ''a''? i really need the value. :( so please if you know the code share it to me.

[Oleg Komarov]

Grzegorz has given you a valid solution. If you really needed the value you wouldn't have posted the comment in the first place since it's in the code.

[Ejay Kasai]

i mean i need a code to evaluate the area between the two curves. i need to make a matlab program for that.

[Walter Roberson]

The expression Grzegorz gave, a = trapz(x,y2)-trapz(x,y1) *is* the code to evaluate the area between the two curves. This is elementary calculus: the area between two curves is the difference between their integrals. trapz() calculates numeric integrals.

Answer 2

[Shyam babu]

find the area included between the curves y^2=4*x & x^2=4*y

[Walter Roberson]

I do not seem to understand how this would solve the question posted by @Ejay Kasai ??