Question 7 - A-Level Maths

Exam Board	Edexcel
Module	AS Paper 1 (AS Paper 1)
Year	2020
Session	June
Topic	Indefinite & Definite Integrals

Given that $k$ is a positive constant and $\int _ { 1 } ^ { k } \left( \frac { 5 } { 2 \sqrt { x } } + 3 \right) \mathrm { d } x = 4$
1. show that $3 k + 5 \sqrt { k } - 12 = 0$
2. Hence, using algebra, find any values of $k$ such that
$$\int _ { 1 } ^ { k } \left( \frac { 5 } { 2 \sqrt { x } } + 3 \right) \mathrm { d } x = 4$$