Note: the challenge problems are being graded on process as much as results. Therefore, please show your work and explain your reasoning as much as possible. Partial credit will be given. Exact answers are preferred, but approximate answers are acceptable $-$ particularly if finding an exact answer is infeasible.

Let $R$ be the region bounded by the $x-$axis, the lines $y=2$ and $y=5,$ and the curve $y=\frac{1}{x^2}.$

Find the real number a such that the line $y=$a cuts $R$ into two regions of equal area.

Find the real number $b$ such that the line $x=b$ cuts $R$ into two regions of equal area.

Find the real number $c$ such that the line $y=cx$ cuts $R$ into two regions of equal area. $($Do step by step write them out$)$ So i can understand it better