Đáp án:
\[a = \frac{{1 - \pi }}{{2\pi }}\]
Giải thích các bước giải:
\(\begin{array}{l}
\int\limits_0^{\frac{1}{2}} {\cos \left( {\pi x} \right)dx} = \mathop {\left. {\frac{1}{\pi }.\sin \left( {\pi x} \right)} \right|}\nolimits_0^{\frac{1}{2}} \\
= \frac{1}{\pi }.\left( {\sin \frac{\pi }{2} - \sin 0} \right)\\
= \frac{1}{\pi }\left( {1 - 0} \right) = \frac{1}{\pi }\\
\Rightarrow 2a + 1 = \frac{1}{\pi } \Leftrightarrow 2a = \frac{1}{\pi } - 1 \Leftrightarrow 2a = \frac{{1 - \pi }}{\pi } \Leftrightarrow a = \frac{{1 - \pi }}{{2\pi }}
\end{array}\)
