# To find intersection, and to calculate the area between two curves for two functions.

18 views (last 30 days)

Show older comments

VIDHYA HARINI
on 7 Jan 2023

Commented: Walter Roberson
on 8 Jan 2023

This question was flagged by Star Strider

Hi everyone, kindly please help me in solving this problem. I am new to this matlab. So I am not really sure how to do this.

Hoping for a step-by-step answer.

Let f(x) = e^x - 1 and g(x) = 1 - x^2 for x ∈ [0; 1]. Draw the graphs of the two functions f and g, determine the point of intersection z of the two graphs and calculate the area of the region between the two graphs in [0; z].

Thank you in advance.

##### 2 Comments

Walter Roberson
on 7 Jan 2023

### Accepted Answer

Sulaymon Eshkabilov
on 7 Jan 2023

Edited: Sulaymon Eshkabilov
on 7 Jan 2023

Step 1. Calculation the two functions

x = linspace(0, 1, 200);

f = exp(x)-1;

g = 1-x.^2;

Step 2. Plot the calculated f(x) and g(x) points

plot(x, f, 'b-', x, g, 'r', LineWidth=2), grid on

xlabel('$x$', 'interpreter', 'latex')

ylabel('$f(x), \ g(x)$', 'interpreter', 'latex')

title 'Area between two curves', hold on

Step 3. Find the intersection

[xi,yi] = polyxpoly(x,f,x,g);

mapshow(xi,yi,'DisplayType','point','Marker','o', 'MarkerFaceColor', 'c', 'MarkerSize', 9)

Step 4. Compute the area between the two curves

AREA = trapz(x,f)-trapz(x,g)

##### 4 Comments

Walter Roberson
on 8 Jan 2023

The area "between" the two curves is the sum:

- area of (higher one minus lower one) between 0 and intersection point; plus
- area of (new higher one minus new lower one) between intersection point and 1.

Which can also be expressed as the absolute value of the difference in the functions.

The calculation you did is the plain difference between the functions -- and the difference goes negative when the functions intersect.

syms t

AREA = int(abs((exp(t)-1) - (1-t.^2)), 0, 1)

vpa(AREA)

### More Answers (0)

### See Also

### Categories

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!