I can't find the upper or lower boundaries for P to even begin the question
For region \(P\), you can observe that the "endpoints" of the region are both cut off by the line \(y=e\). For \(y=e^x\), the endpoint at \((1,e)\) is literally plotted for you.
For the left "endpoint", you can simply find the point of intersection between the line \(y=e\) and the curve \(y=e^{-x}\).
\begin{align*}
e &= e^{-x}\\
1 &= -x\\
x &= -1
\end{align*}
So the left "endpoint" is at \((-1, e)\).
However, incidentally enough the easier of the two is the area of region \(Q\) here. For region \(P\), you should identify a region split at \(x=0\), i.e. along the \(y\)-axis.
You should double check the diagram, and observe that:
- For \(x\in [-1,0]\), the upper curve is the line \(y=e\), but the lower curve is \(y=e^{-x}\).
- For \(x\in [0,1]\), the upper curve is the line \(y=e\), but the lower curve is \(y=e^x\).
This results in two separate integrals that you have to evaluate for this problem. You should use the above information to consider what they are.