In the diagram, the curve $y=3\ln(x-2)$ cuts the $x$-axis at $Q$. A line which meets the curve

Question

In the diagram, the curve $y=3\ln(x-2)$ cuts the $x$-axis at $Q$. A line which meets the curve at $P(5, p)$ cuts the $x$-axis at $(8, 0)$. State the exact coordinates of $Q$ and $P$. Calculate the exact area bounded by the curve, the line and the $x$-axis.

Accepted Answer

(a) $Q=(3,0),\ P=(5,3\ln3)$ (b) $\frac{27}{2}\ln3-6\text{ units}^2$

Integration - Area under Logarithmic Curve

Integration - Area under Logarithmic Curve

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