Question 10 - A-Level Maths

Exam Board	Edexcel
Module	Paper 2 (Paper 2)
Year	2023
Session	June
Topic	Integration with Partial Fractions

$\mathrm { f } ( x ) = \frac { 3 k x - 18 } { ( x + 4 ) ( x - 2 ) } \quad$ where $k$ is a positive constant
1. Express $\mathrm { f } ( x )$ in partial fractions in terms of $k$.
2. Hence find the exact value of $k$ for which
$$\int _ { - 3 } ^ { 1 } f ( x ) d x = 21$$