Show that \(\dfrac{\mathrm d}{\mathrm dx}\left(\dfrac{2x+5}{\sqrt{x-2}}\right)=\dfrac{2x-13}{2\sqrt{(x-2)^3}}\).[3]
The diagram shows part of the curve \(y=\dfrac{5(2x-13)}{\sqrt{(x-2)^3}}\) where \(x>0\). The curve intersects the \(x\)-axis at point \(A\). The line \(x=18\) cuts the curve at point \(B\). Find, using part (a), the area bounded by the curve and line \(AB\). Show all necessary working. Leave your answer correct to 2 decimal places.[6]
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