The area bounded by the loop of the curve ${{y}^{2}}={{\left( 1-x \right)}^{2}}\left( x+3 \right)$

Question

The area bounded by the loop of the curve ${{y}^{2}}={{\left( 1-x \right)}^{2}}\left( x+3 \right)$ is given by $2\displaystyle\displaystyle \displaystyle\int_{\alpha }^{\beta }{\left( 1-x \right)}\sqrt{x+3}\ \mathrm{d}x$. State the values of $\alpha $ and $\beta $.[1] Use the substitution $u=\sqrt{x+3}$ to find the exact area bounded by this loop.[4]

Accepted Answer

(a) $\alpha=-3$, $\beta=1$ (b) $\dfrac{256}{15}\text{ units}^2$

2024 NYJC P2 Q1

2024 NYJC P2 Q1

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