The region $R_2$ , also shown shaded in the figure, is bounded by $C$ , the $x$ -axis and $l$ . Given that the area of $R_1$ is equal to the area of $R_2$ ,

find the exact value of $m$ .

[3]

1.11.3 Definite integrals and areas Questions

A Level
Maths
1.11.3 Definite integrals and areas

A Level
Maths AQA
Question bank

1.11.3 Definite integrals and areas

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Question 18

The figure shows

the curve $C$ with equation $y = 2x - x^2$
the line $l$ with equation $y = m x$ , where $m$ is a constant and $0 < m < 2$

The line and the curve intersect at the origin $O$ and at the point $P$ .

Find, in terms of $m$ , the coordinates of $P$ .

[2]

The region $R_1$ , shown shaded in the figure, is bounded by $C$ and $l$ .

Show that the area of $R_1$ is

\frac{(2 - m)^3}{6}

[3]

The region $R_2$ , also shown shaded in the figure, is bounded by $C$ , the $x$ -axis and $l$ . Given that the area of $R_1$ is equal to the area of $R_2$ ,

find the exact value of $m$ .

[3]

1.11.3 Definite integrals and areas Questions

A Level
Maths
1.11.3 Definite integrals and areas