<p>The diagram shows part of the curve \(y=e^{\left(-\frac{1}{2}x+2\right)}+x-1\) that intersects the \(y\)-axis at \(R\). The tangent to the curve at \(P(4,4)\) intersects the \(y\)-axis at \(Q\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1772346671728-x1yfki9y7f.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Show that the area of the shaded region can be expressed as&nbsp;\(ae^2+b\) where&nbsp;\(a\) and \(b\) are constants to be determined.<span class="inline-marks">[8]</span></p>

The diagram shows part of the curve \(y=e^{\left(-\frac{1}{2}x+2\right)}+x-1\) that intersects the \(y\)-axis at \(R\). The tangent to the curve at \(P(4,4)\) intersects the \(y\)-axis at \(Q\).

Show that the area of the shaded region can be expressed as \(ae^2+b\) where \(a\) and \(b\) are constants to be determined.

2025 CHS PRELIMS P2 Q11

2025 CHS PRELIMS P2 Q11