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.

[4]

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

A Level
Maths CCEA
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1.1.10 Algebra and functions

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Question 58

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 $D = 0$ .

[4]

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.

[4]

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions