9758/2019/P1/Q02

The curve $C$ has equation $y=x^{3}+x-1$.

(i) $C$ crosses the $x$-axis at the point with coordinates $(a, 0)$. Find the value of $a$ correct to 3 decimal places.

[1]

(ii) You are given that $b>a$.

The region $P$ is bounded by $C$, the $x$-axis and the lines $x=-1$ and $x=0$. The region $Q$ is bounded by $C$, the line $x=b$ and the part of the $x$-axis between $x=a$ and $x=b$. Given that the area of $Q$ is 2 times the area of $P$, find the value of $b$ correct to 3 decimal places.

[4]