Tính các tích phân sau: a) tích phân pi/2 0 (3cosx + 2sinx) dx; b) tích phân pi/4 pi/6 (1 / cos^2 x - 1/ sin^2 x

a) \(\int\limits_0^{\frac{\pi }{2}} {\left( {3\cos x + 2\sin x} \right)dx} \) = \(\int\limits_0^{\frac{\pi }{2}} {3\cos xdx}  + \int\limits_0^{\frac{\pi }{2}} {2\sin xdx} \)

                                        = \(\left. {3\sin x} \right|_0^{^{\frac{\pi }{2}}} - \left. {2\cos x} \right|_0^{^{\frac{\pi }{2}}}\)

                                        = \(3\sin \frac{\pi }{2} - 3\sin 0 - 2\cos \frac{\pi }{2} + 2\cos 0\)

                                        = 5.

b) \(\int\limits_{\frac{\pi }{6}}^{\frac{\pi }{4}} {\left( {\frac{1}{{{{\cos }^2}x}} - \frac{1}{{{{\sin }^2}x}}} \right)dx} \) = \(\int\limits_{\frac{\pi }{6}}^{\frac{\pi }{4}} {\frac{1}{{{{\cos }^2}x}}dx}  - \int\limits_{\frac{\pi }{6}}^{\frac{\pi }{4}} {\frac{1}{{{{\sin }^2}x}}dx} \)

                                       = \(\left. {\tan x} \right|_{_{\frac{\pi }{6}}}^{^{\frac{\pi }{4}}} - \left. {\cot x} \right|_{_{\frac{\pi }{6}}}^{^{\frac{\pi }{4}}}\)

                                       = \(\tan \frac{\pi }{4} - \tan \frac{\pi }{6} - \cot \frac{\pi }{4} + \cot \frac{\pi }{6}\)

                                       = 2 − \(\frac{{4\sqrt 3 }}{3}\).