Question

Найдите числа A и B, при каких функция f(x) удовлетворяет следующим условиям?

Answer 1

 $y'=A*sin(\pi\*x)+B=\pi\*A*cos(\pi\*x) \\ \int\limits^2_0 {\pi\*A*cos(\pi\*x)} \, dx = Bx-\frac{A*cos(\pi\*x)}{\pi}\\\\ y'(1)=\pi\*A*cos(\pi)=2\\ A=\frac{-2}{\pi}\\ 2B-\frac{\frac{-2}{\pi}}{ \pi } + \frac{\frac{2}{\pi}}{\pi} = 4\\ 2B+\frac{4}{\pi^2} = 4\\ B=2(1-\frac{1}{\pi^2})\\\\ A+B=-\frac{2\pi}{\pi^2}+2-\frac{2}{\pi^2} = 2-\frac{2\pi+2}{\pi^2}$