1.11 H: Integration

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Question 92

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 $P$ .

Coordinate diagram showing the parabola C, the line l through O and P, and hatched regions R1 and R2.

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]

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 $P$ .

Coordinate diagram showing the parabola C, the line l through O and P, and hatched regions R1 and R2.

1.11 H: Integration

Question 92

Markscheme

1.11 H: Integration

Question 92

Markscheme

1.11 H: Integration

Question 92

1.11 H: Integration Questions

1.11 H: Integration

Question 92

1.11 H: Integration Questions