CAIE A-Level Mathematics A2 3.5.4 An Integrand of the Form X Questions

Practise recognising and integrating standard trigonometric, logarithmic and rational integrand forms.

Exam points

[Maximum number: 4]

Let $\mathrm{f}(x)=\frac{\cos x}{1+\sin x}$ .

Find $\int_{\frac{1}{6} \pi}^{\frac{1}{2} \pi} \mathrm{f}(x) \mathrm{d} x$ . Give your answer in a simplified exact form.

State integral of the form $a \ln (1+\sin x)$

*M1

State correct integral $\ln (1+\sin x)$
Use limits correctly
Obtain answer $\ln \frac{4}{3}$

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