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.

1.1 Algebra and functions

Question 117

Markscheme

1.1 Algebra and functions

Question 117

Markscheme

1.1 Algebra and functions

Question 117

1.1 Algebra and functions Questions

1.1 Algebra and functions

Question 117

1.1 Algebra and functions Questions