How to sketch the region enclosed by the given curves and compute it's area

I'm given

x=y^4

y=sqrt(2-x)

y=0

and need to find the area of the region enclosed by the curves

[Ameer Hamza]

Is this a homework problem? What have you tried already? https://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Kiley Foulke]

It's for a virtual study hall, I've tried google, I've been through a bunch of MATLAB answers and can't seem to find what I'm looking for. I've tried area, plotting, trapz, cumtrapz

Answer 1

[Shubham Khatri]

The fplot function can be used to solve it. By solving equations, we can see that the intersection point is at (1,0). To compute the area, we can calculate the area under the curve for fun2 till x=1 and add it to area under the curve from x=1 to x=2 for fun 1. Please have a look at the following code.

fplot(@(x) x.^0.25); %ploting x.^0.25
hold on
fplot(@(x) sqrt(2-x)); %ploting sqrt(2-x)
fun1 = @(x) sqrt(2-x); %defining function sqrt(2-x) for integration
fun2 = @(x) x.^0.25; %defining function X.^0.25 for integration
r = integral(fun2,0,1) %integration from 0 to 1
q = integral(fun1,1,2) % integration from 1,2
Area=r+q %computing the area  

For more information, please click fplot integral