(i)[4]
Find the exact $x$-coordinate of $M$.
(ii)[6]
Calculate the value of $p$ such that the area of $R$ is equal to $1$. Give your answer correct to $3$ significant figures.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram depicts the curve $y = \frac{x^2}{1 + x^3}$ for $x \ge 0$, together with its maximum point $M$. The shaded area $R$ is bounded by the curve, the $x$-axis, and the straight lines $x = 1$ and $x = p$.