[问答题]
$\text { Let } f(x)=e^{x} \sin (\pi x)+4 \text {, for } 0 \leq x \leq 2 \text {. The graph of } f \text { is given below. }$
There is an x -intercept at the point P , a local maximum point at A , where x=a , and a local minimum point at B , where x=b .
1. Write down the x -coordinate of P .
2. Find the value of a and the value of b .
3. Find $ \int_{a}^{b} f(x) \mathrm{d} x$ . Explain why this is not the area of the shaded region.
