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

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Kiley Foulke
Kiley Foulke 2020-10-6
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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回答（1 个）

Shubham Khatri
Shubham Khatri 2020-10-9
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

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