Find points of intersection and area between two curves,

Hi all,

Being reasonably new to Matlab I'm stuck on how to find both answers. I can plot the two curves on a graph but don't know how to calculate points of intersection and area between them. The curves concerned are as follows:

y = (3x^2)+2x-10

       &

y = sin(5x+c2) when c2=9 (c2 calculated in a previous question)

any advice would be great, thanks!

Answer 1

[Star Strider]

I would use the fzero function to calculate the intersections:

x = linspace(-3,3);
y1 = @(x) (3*x.^2)+2.*x-10;
c2=9;
y2 = @(x) sin(5*x+c2);

for k1 = 1:2
    x0 = 5*(-1)^k1;
    xint(k1) = fzero(@(x) y1(x)-y2(x), x0);
end

figure(1)
plot(x, y1(x))
hold on
plot(x, y2(x))
plot(xint, y1(xint), 'pb')
grid

I will leave the area calculation to you.

Answer 2

[Liam Nolan]

OK thank you, but how do I obtain an exact value for the intersection points rather then just estimating it by reading it off the graph?

[Star Strider]

The ‘xint’ vector has the x-coordinates of the intersections. Since they are common to both curves, you can find the y-values by substituting in either function. In the ‘figure(1)’ plot, I did this with ‘y1(xint)’.

Run my code (copy it and paste it to your MATLAB Editor) to see how it works.

The integral is easy to calculate, using a similar idea to what I did in the fzero call. (I already did it.) Give it a go, and if you have problems, I’ll help you get it running.

Answer 3

[Liam Nolan]

I understand it's not 100% exact points but just i need to obtain the coordinates for them

[Torsten]

Did you even take a look in Start Strider's code ?

xint(1) and xint(2) are the intersection points of the two curves.

Best wishes

Torsten.

[Star Strider]

Thank you, Torsten.

Answer 4

[Liam Nolan]

As I said I'm reasonably new to matlab and didn't know you could just type xint(1) after to get the exact value... but now I do, thanks all!

[Star Strider]

My pleasure!