Задача 53243 ...

5f50db49869d6262826fbda1

09.09.2020 08:34:43

-1/2 ∫ cos(0,5x)dx

5f3ea7e3faf909182968ddd9

09.09.2020 11:10:55

[m]-\frac{1}{2}\int cos0,5xdx= [/m]

[i]Замена переменной:[/i]
[i]0,5x=t[/i]
[i]x=2t[/i]
[i]dx=2dt[/i]

[m]=-\frac{1}{2}\int cost \cdot 2dt= -\frac{1}{2}\cdot 2\int cost dt = [/m]

=[m]-\int cost dt =- sint + C [/m]

Обратный переход от t к х:

[i]t=0,5x[/i]

[m]=- sin0,5x + C [/m]

О т в е т. [m]=- sin0,5x + C [/m]