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Show that, by evaluating the integral, $$\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \left(4\cos^2 2x + \frac{1}{\cos^2 x}\right) \, dx = 4\sqrt{3} + \frac{\pi}{6} - 1.$$
Mathematics 9709 · AS & A Level · Integration
Mathematics 9709 · AS & A Level · Integration
Show that, by evaluating the integral, $$\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \left(4\cos^2 2x + \frac{1}{\cos^2 x}\right) \, dx = 4\sqrt{3} + \frac{\pi}{6} - 1.$$