Tìm hai số thực A,B sao cho

\[\begin{array}{*{20}{l}}{f(x) = A\sin \pi x + B \Rightarrow f'(x) = A\pi \cos \pi x}\\{f'(1) = 2 \Rightarrow A\pi \cos \pi = 2 \Rightarrow A = - \frac{2}{\pi }}\end{array}\]

\[\mathop \smallint \limits_0^2 f(x)dx = 4 \Rightarrow \mathop \smallint \limits_0^2 (A\sin \pi x + B)dx = 4\]

\[ \Rightarrow - \frac{A}{\pi }\cos 2\pi + 2B + \frac{A}{\pi }\cos 0 = 4 \Rightarrow B = 2\]