Question 5 - A-Level Maths

Exam Board	AQA
Module	FP1 (Further Pure Mathematics 1)
Year	2010
Session	January
Topic	Sequences and series, recurrence and convergence

Explain why \(\int _ { 0 } ^ { \frac { 1 } { 16 } } x ^ { - \frac { 1 } { 2 } } \mathrm {~d} x\) is an improper integral.
For each of the following improper integrals, find the value of the integral or explain briefly why it does not have a value:
1. \(\int _ { 0 } ^ { \frac { 1 } { 16 } } x ^ { - \frac { 1 } { 2 } } \mathrm {~d} x\);
2. \(\int _ { 0 } ^ { \frac { 1 } { 16 } } x ^ { - \frac { 5 } { 4 } } \mathrm {~d} x\).