The cross-section of a industrial drainage channel is modeled by a curve $C\,$ with equation

\frac{(x - k)^2}{\sqrt{x}}, \quad x > 0

where $k\,$ is a positive constant.

Show that

\int_{1}^{16} \frac{(x - k)^2}{\sqrt{x}} \, dx = ak^2 + bk + \frac{2046}{5}

where $a\,$ and $b\,$ are integers to be found.

A sketch of the curve $C\,$ and a straight line $l\,$ are shown. The line $l\,$ represents the water level during a flood, intersecting the curve $C\,$ at point $A (1, 9)$ and at point $B (16, q)$ , where $q\,$ is a constant.

Show that $k = 4$ .

Sketch of curve C and straight line l intersecting at A(1, 9) and B(16, q), with region R between them.

The region $R\,$ is the cross-sectional area of the water, bounded by the curve $C\,$ and the line $l\,$ between points $A\,$ and $B$ . Using the results from parts (a) and (b),

find the area of region $R$ .

The cross-section of a industrial drainage channel is modeled by a curve $C\,$ with equation

\frac{(x - k)^2}{\sqrt{x}}, \quad x > 0

where $k\,$ is a positive constant.

Show that

\int_{1}^{16} \frac{(x - k)^2}{\sqrt{x}} \, dx = ak^2 + bk + \frac{2046}{5}

where $a\,$ and $b\,$ are integers to be found.

Show that $k = 4$ .

Sketch of curve C and straight line l intersecting at A(1, 9) and B(16, q), with region R between them.

The region $R\,$ is the cross-sectional area of the water, bounded by the curve $C\,$ and the line $l\,$ between points $A\,$ and $B$ . Using the results from parts (a) and (b),

find the area of region $R$ .

1.8 Integration

Question 62

Markscheme

1.8 Integration

Question 62

Markscheme

1.8 Integration

Question 62

1.8 Integration Questions

1.8 Integration

Question 62

1.8 Integration Questions