The diagram shows part of the curve $y=\dfrac{4-x}{\sqrt{x+1}}$, which meets the positive $x$-ax

Question

The diagram shows part of the curve $y=\dfrac{4-x}{\sqrt{x+1}}$, which meets the positive $x$-axis at $A$. Find the exact area of the shaded region bounded by the curve and the coordinate axes.[5]

Accepted Answer

$\dfrac{20\sqrt5-28}{3}\text{ units}^2$

Radical curve ending at the x-axis

Radical curve ending at the x-axis

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