Integration - Area under Logarithmic Curve
Integration - Area under Logarithmic Curve
IB AA SL: core and optional content
Core: find p and q. Optional: exact logarithmic area without a supplied antiderivative.
In the diagram, the curve \(y = \ln(x - 1)\) cuts the \(x\)-axis at \(Q(q, 0)\) and passes through the point \(P(3, p)\).
- State the exact value of \(p\) and of \(q\).
- Calculate the exact area of the shaded region.
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Answer:(a) \(p=\ln2\), \(q=2\) (b) \(2\ln2-1\text{ units}^2\)
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