Find the area enclosed by the given curves

Question

x=y

x=y^2

Answer 1

We need to first find the bounds by equating the expression represented by x.

 

y = y²

 

0 = y² - y

 

0 =y(y - 1)

 

y = 0          and        y = 1

 

 

Now we can set up the definite integral to find the area.

 

∫(y² - y)dy

 

lower bound = 0

upper bound = 1

 

 

Evaluate the definite integral to get your area.