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Let \(f(x) = e^x Sin 2x + 10\), with \(0 \leq x \leq 4\).

Part of the graph of \(f\) is shown below.

The figure is not to scale.

Shown are an x-intercept at point \(A\), a local maximum at point \(M\) with \(x = p\) and a local minimum at point \(N\) with \(x = q\).

1. State the x-coordinate of \(A\).

2. Find the value of

   1. \(p\)
   2. \(q\)

3. Find \(\int_p^qf(x)dx\).

   Explain why this is not the area of the shaded region.