Hi everyone. I tried solving this problem:

"Get the area of the region bounded by the upper branch of the parabola x=y^{2}, the tangent line to the parabola at (1,1) and the x-axis."

Attached is a picture of my solution to the problem. I just want to ask if I did the right thing, and if not, what did I do wrong and how do I fix it?

Thank you very much for your help!