The curve $y=\dfrac{4}{\sqrt{x+1}}$ meets the line $y=2$ at $A$. Find the coordinates of $A$

Question

The curve $y=\dfrac{4}{\sqrt{x+1}}$ meets the line $y=2$ at $A$. Find the coordinates of $A$.[2] Hence find the area of the shaded region bounded by the curve, the line and the $y$-axis.[4]

Accepted Answer

(i) $A=(3,2)$ (ii) $2\text{ units}^2$

Radical curve above a horizontal line

Radical curve above a horizontal line

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