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

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Kiley Foulke 2020-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/606236-how-to-sketch-the-region-enclosed-by-the-given-curves-and-compute-it-s-area

回答： Shubham Khatri 2020-10-9

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

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Ameer Hamza 2020-10-6

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 2020-10-6

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

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Answer 1

Shubham Khatri 2020-10-9

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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  