9709 P31 - Nov 2019 - Q6
1754
(i) By differentiating \(\frac{\cos x}{\sin x}\), show that if \(y = \cot x\) then \(\frac{dy}{dx} = -\csc^2 x\).
(ii) Show that \(\int_{\frac{1}{4}\pi}^{\frac{1}{2}\pi} x \csc^2 x \, dx = \frac{1}{4}(\pi + \ln 4)\).
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