AQA FP1 — Question 2

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
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TopicIndefinite & Definite Integrals
2
  1. For each of the following improper integrals, find the value of the integral or explain briefly why it does not have a value:
    1. \(\int _ { 0 } ^ { 9 } \frac { 1 } { \sqrt { x } } \mathrm {~d} x\);
    2. \(\int _ { 0 } ^ { 9 } \frac { 1 } { x \sqrt { x } } \mathrm {~d} x\).
  2. Explain briefly why the integrals in part (a) are improper integrals.
2 (a) For each of the following improper integrals, find the value of the integral or explain briefly why it does not have a value:\\
(i) $\int _ { 0 } ^ { 9 } \frac { 1 } { \sqrt { x } } \mathrm {~d} x$;\\
(ii) $\int _ { 0 } ^ { 9 } \frac { 1 } { x \sqrt { x } } \mathrm {~d} x$.\\
(b) Explain briefly why the integrals in part (a) are improper integrals.

\hfill \mbox{\textit{AQA FP1  Q2}}
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