| Exam Board | SPS |
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| Module | SPS SM Pure (SPS SM Pure) |
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| Year | 2023 |
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| Session | February |
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| Topic | Integration by Substitution |
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10.
a) Show that
$$\int _ { 0 } ^ { \frac { \pi } { 3 } } \frac { 4 \sin x } { 1 + 2 \cos x } \mathrm {~d} x = \ln a$$
where \(a\) is a rational constant to be found.
b) By using a suitable substitution, find the exact value of
$$\int _ { 0 } ^ { \sqrt { 3 } } \frac { 1 } { \left( 4 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } d x$$