Find the equation of the line that passes trough point (0,1) such that the area, S, of the region enclosed by this line and the parabola y=x^2 is (5√5)/6.
This is what I did:
I found the equation of the line which is y=x+1
Then, I put x^2=x+1
S=integral of (x+1-x^2)dx [α,β].
It gave me (5√5)/6.
I don't know how to continue to find out the equation.
Please help me!