OCR C4 2008 January — Question 10

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2008
SessionJanuary
TopicIntegration by Substitution
10
  1. Use the substitution \(x = \sin \theta\) to find the exact value of $$\int _ { 0 } ^ { \frac { 1 } { 2 } } \frac { 1 } { \left( 1 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } \mathrm {~d} x$$
  2. Find the exact value of $$\int _ { 1 } ^ { 3 } \frac { \ln x } { x ^ { 2 } } \mathrm {~d} x$$ 4
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