Question 2 - A-Level Maths

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2014
Session	June
Topic	Indefinite & Definite Integrals

Find \(\int \left( 1 + 3 x ^ { \frac { 1 } { 2 } } + x ^ { \frac { 3 } { 2 } } \right) \mathrm { d } x\).
1. The expression \(( 1 + y ) ^ { 3 }\) can be written in the form \(1 + 3 y + n y ^ { 2 } + y ^ { 3 }\). Write down the value of the constant \(n\).
2. Hence, or otherwise, expand \(( 1 + \sqrt { x } ) ^ { 3 }\).
Hence find the exact value of \(\int _ { 0 } ^ { 1 } ( 1 + \sqrt { x } ) ^ { 3 } \mathrm {~d} x\).