1.8 Integration

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Question 61

Find

\int \frac{(4-3x)^2}{5\sqrt{x}} \, dx, \quad x > 0

giving your answer in simplest form.

[4]

ii.

The rate of change of the depth of water, $D$ metres, in a reservoir with respect to time $t$ days is modeled by the equation $dDdt=t2+at+b\frac{dD}{dt} = t^2 + at + b$ for $\le t \le 10$ , where $a$ and $b$ are constants.

At the start of a monitoring period ( $t = 0$ ), the depth is 15 metres.
After 3 days, the depth has fallen to 9 metres.
On the 3rd day ( $t = 3$ ), the depth is decreasing at a rate of 2 metres per day.

Determine the expression for $D$ in terms of $t$ , giving your answer in simplest form.

[7]

Find

\int \frac{(4-3x)^2}{5\sqrt{x}} \, dx, \quad x > 0

giving your answer in simplest form.

[4]

At the start of a monitoring period ( $t = 0$ ), the depth is 15 metres.
After 3 days, the depth has fallen to 9 metres.
On the 3rd day ( $t = 3$ ), the depth is decreasing at a rate of 2 metres per day.

Determine the expression for $D$ in terms of $t$ , giving your answer in simplest form.

1.8 Integration

Question 61

Markscheme

1.8 Integration

Question 61

Markscheme

1.8 Integration

Question 61

1.8 Integration Questions

1.8 Integration

Question 61

1.8 Integration Questions