Question 1 - A-Level Maths

Exam Board	CAIE
Module	Further Paper 2 (Further Paper 2)
Year	2023
Session	June
Topic	Taylor series
Type	Use series to approximate integral

Find the Maclaurin series for \(\sin ^ { - 1 } x\) up to and including the term in \(x ^ { 3 }\).
Deduce an approximation to \(\int _ { 0 } ^ { \frac { 1 } { 5 } } \frac { 1 } { \sqrt { 1 - u ^ { 2 } } } \mathrm {~d} u\), giving your answer as a fraction.