Show that the first two terms of the binomial expansion of \(\sqrt { 4 - 2 x ^ { 2 } }\) are
$$2 - \frac { x ^ { 2 } } { 2 }$$
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State the range of values of \(x\) for which the expansion found in part (a) is valid. [0pt]
[2 marks]
9
Hence, find an approximation for
$$\int _ { 0 } ^ { 0.4 } \sqrt { \cos x } \mathrm {~d} x$$
giving your answer to five decimal places.
Fully justify your answer.
9
A student decides to use this method to find an approximation for
$$\int _ { 0 } ^ { 1.4 } \sqrt { \cos x } \mathrm {~d} x$$
Explain why this may not be a suitable method.