Integral: x = y^2 - Solving the Mystery

[Miike012]

How does the function equal x = y^2 I though it was y = x^1/2 ??
I highlighted this part in the picture I posted

 

[Frogeyedpeas]

Why don't you see if those two are equal?

Try graphing them both

 

[I like Serena]

Hi Miike012!

What do you get if you square both sides of y = x^1/2?

 

[Miike012]

Ok yes that's true.. I guess what I am really asking my self is why did they go with x = y^2 instead of y = x^1/2.

 

[I like Serena]

Can I assume this is about integrals?

The white area is calculated using the integral of y(x)=x^1/2.
This integral calculates the area between the graph and the x-axis.

To calculate the gray area, basically the axes are swapped around, so the integral between the graph and the y-axis can be calculated.
But if you do that, the function has to be inverted as well.