Question

The region bounded below by the parabola y=x^2+4 and above by the line y=8 is partitioned into two subsections of equal area by cutting it across with the horizontal line y=c. Find C

Answer 1

there's symmetry about the y-axis, so
\[\int\limits_{0}^{\sqrt{c-4}}(c-(x^2+4))dx = \int\limits_{0}^{2}(8-c)dx\]

Answer 2

\[(cx-\frac{ x^3 }{ 3 }-4x)|_{0}^{\sqrt{c-4}}=(8x-cx)|_{0}^{2}\]

Answer 3

anyone else?