Shaded Area

For this I would name two graphs as 1 and 2. So, $Graph_1:x=y^n$ $Graph_2:y=x^n$ Area under $graph_1$ will be the area under $y-axis$ , $Area=\int _0^1y^ndy$ $Area=\frac{1}{n+1}$ Similarly area under $graph_2$ will be area under $x-axis$ , $Area=\int _0^1x^ndx$ $Area=\frac{1}{n+1}$ By adding up areas we get, $Area=\frac{2}{\left(n+1\right)}$ $\frac{1}{1009}=\frac{2}{\left(n+1\right)}$ $n=2017$ I didn't knew this problem was linked with new year BTW Happy New Year 2017!