Solve for Y-Coordinates of Intersection | Simple Problem with f(y) and g(y)

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Simple problem...need help PlEaSe!

Homework Statement


Okay so I am trying to find the area of a region but I having a problem with a simple intermediate step! I have...
f(y) = y^2
g(y) = y + 2
I need to find the y-coordinates of where the 2 lines intersect. Can someone please help me?


Homework Equations





The Attempt at a Solution

 
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Set them equal to each other and solve for y.
 
At the point of intersection, y2= y+ 2. Solve y2- y- 2= 0.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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