The curve $C$ is defined by the parametric equations
$x=2t-2\ln \left( t+1 \right)+2$, $y=-2t-2\ln \left( t+1 \right)+1$ where $t>-1$.
Another curve $L$ is defined by the equation $x=2{{\left( y+1 \right)}^{2}}-6$. The graphs of $C$ and $L$intersect at the point $A\left( 2,1 \right)$ as shown in the diagram below.
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Find the area of the shaded region bounded by $C$, $L$ and the line $y=-1-\ln 4$, express your answer in the form $\frac{62}{3}+4A-2{{A}^{2}}-\frac{16{{A}^{3}}}{3}$, where $A$ is an exact real constant.[6]

The curve $C$ is defined by the parametric equations

$x=2t-2\ln \left( t+1 \right)+2$, $y=-2t-2\ln \left( t+1 \right)+1$ where $t>-1$.

Another curve $L$ is defined by the equation $x=2{{\left( y+1 \right)}^{2}}-6$. The graphs of $C$ and $L$intersect at the point $A\left( 2,1 \right)$ as shown in the diagram below.

Find the area of the shaded region bounded by $C$, $L$ and the line $y=-1-\ln 4$, express your answer in the form $\frac{62}{3}+4A-2{{A}^{2}}-\frac{16{{A}^{3}}}{3}$, where $A$ is an exact real constant.

2018 SRJC P1 Q5 (ii)

2018 SRJC P1 Q5 (ii)

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