Question 3 - A-Level Maths

Exam Board	OCR
Module	C4 (Core Mathematics 4)
Year	2011
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Find the quotient when $3 x ^ { 3 } - x ^ { 2 } + 10 x - 3$ is divided by $x ^ { 2 } + 3$, and show that the remainder is $x$.
Hence find the exact value of $$\int _ { 0 } ^ { 1 } \frac { 3 x ^ { 3 } - x ^ { 2 } + 10 x - 3 } { x ^ { 2 } + 3 } \mathrm {~d} x$$