2026 NORTHBROOKS P1 Q13

The diagram shows part of the curve \(y=\mathrm e^{-x/2}\).

The tangent to the curve at \(A(-4,\mathrm e^2)\) meets the \(x\)-axis at \(B\).

Find the area of the shaded region bounded by the curve, the tangent to the curve at \(A\), the line \(x=3\) and the \(x\)-axis.[8]