Giải thích các bước giải:
a,
\(\begin{array}{l}
\int\limits_0^{\frac{\pi }{4}} {\sin 2x.\cos xdx} \\
= \int\limits_0^{\frac{\pi }{4}} {2\sin x.\cos x.\cos xdx} \\
= 2\int\limits_0^{\frac{\pi }{4}} {{{\cos }^2}x.\sin xdx} \\
= - 2\int\limits_0^{\frac{\pi }{4}} {{{\cos }^2}x.d\left( {\cos x} \right)} \\
= \mathop { - 2.\frac{{{{\cos }^3}x}}{3}}\nolimits_0^{\frac{\pi }{4}}
\end{array}\)
c,
\(\begin{array}{l}
\int\limits_0^{\frac{\pi }{4}} {{{\cos }^2}xdx} \\
= \int\limits_0^{\frac{\pi }{4}} {\frac{1}{2}\left( {\cos 2x + 1} \right)dx} \\
= \int\limits_0^{\frac{\pi }{4}} {\frac{1}{2}dx} + \frac{1}{4}\int\limits_0^{\frac{\pi }{4}} {\cos 2x.d\left( {2x} \right)} \\
= \mathop {\left( {\frac{x}{2} + \frac{1}{4}\sin 2x} \right)}\nolimits_0^{\frac{\pi }{4}}
\end{array}\)
