(a)[2]
Demonstrate that $(\sec x + \cos x)^2$ may be written in the form $\sec^2 x + a + b\cos 2x$, with $a$ and $b$ as the constants to determine.
(b)[4]
Hence, find the exact value of $\int_0^{\frac{\pi}{4}} (\sec x + \cos x)^2\, dx$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Once expanded, the integrand should take the form $\sec^2 x + k_1 + k_2\cos2x$” …
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