Integration - Area under Logarithmic Curve

IB AA SL: core and optional content

Core: coordinates p,q. Optional: exact logarithmic area without a supplied antiderivative.

In the diagram, the curve \(y=2\ln(x+3)\) cuts the \(y\)-axis at \((0, q)\). A line, which meets the curve at \((-1, p)\) cuts the \(y\)-axis at \((0, 0.5)\).

1. State the exact value of \(p\) and of \(q\).
2. Calculate the exact area bounded by the curve, the line and the \(y\)-axis.