The rate of mass accumulation in a sediment trap, $M$ (in mg/year), is modeled by the function:

\frac{4t^3 + 5t^2 - 12t + 15}{t^2 + 3}, \quad t \ge 0

where $t\,$ is the time in years since the study began.

Given that

\equiv At + B + \frac{Ct + D}{t^2 + 3}

(i) Find the values of the constants $A$ , $B\,$ and $C$ .

(ii) Show that $D = 0$ .

Hence, using algebraic integration, find the total mass accumulated between $t = 1$ and $t = 3$ , giving your answer in the form $\ln k$ , where $p$ , $q\,$ and $k\,$ are integers and $k\,$ is prime.

The rate of mass accumulation in a sediment trap, $M$ (in mg/year), is modeled by the function:

\frac{4t^3 + 5t^2 - 12t + 15}{t^2 + 3}, \quad t \ge 0

where $t\,$ is the time in years since the study began.

Given that

\equiv At + B + \frac{Ct + D}{t^2 + 3}

(i) Find the values of the constants $A$ , $B\,$ and $C$ .

(ii) Show that $D = 0$ .

Hence, using algebraic integration, find the total mass accumulated between $t = 1$ and $t = 3$ , giving your answer in the form $\ln k$ , where $p$ , $q\,$ and $k\,$ are integers and $k\,$ is prime.

1.3 Functions

Question 145

Markscheme

1.3 Functions

Question 145

Markscheme

1.3 Functions

Question 145

1.3 Functions Questions

1.3 Functions

Question 145

1.3 Functions Questions