The curve $y=\dfrac{18}{(x+1)^2}-1$ cuts the positive $x$-axis at $A$. Find the coordinates of

Question

The curve $y=\dfrac{18}{(x+1)^2}-1$ cuts the positive $x$-axis at $A$. Find the coordinates of $A$.[2] Find the area of the shaded region bounded by the curve, the coordinate axes and the line $x=2$.[4]

Accepted Answer

(i) $A=(3\sqrt2-1,0)$ (ii) $10\text{ units}^2$

Shifted inverse-square curve above the x-axis

Shifted inverse-square curve above the x-axis

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