is this gramaticaly correct : In order to compute the above, we constructed a function, $P(\eta)$, representing the area or integral value of the combined integral for any value of $\eta$ along the interval $[0,1]$, in order to identify its maximum value within the range $0 \leq \eta \leq 1$. Through our detailed exploration, we constructed $P(\eta)$ and identified that its maximum value is $\frac{1}{48}$