Ответ:
[tex]\int\limits_{0}^{\frac{\pi}{2}}x \times \cos{x} dx[/tex]
[tex]\int{x \times \cos{x} }dx[/tex]
[tex]u = x \\ dv = \cos{x}dx[/tex]
[tex]du = dx \\ v = \sin{x}[/tex]
[tex]x \times \sin{x} - \int \sin{x}dx[/tex]
[tex]x \times \sin{x} - ( - \cos{x})[/tex]
[tex]x \times \sin{x} + \cos{x}[/tex]
|-ну пусть это предел будет.
[tex](x \times \sin{x} + \cos{x}){|}^{\frac{\pi}{2}}_{0}[/tex]
[tex] \frac{\pi}{2} \times \sin{ \frac{\pi}{2} } + \cos {\frac{\pi}{2} } - (0 \sin{0} + \cos{0})[/tex]
[tex] \frac{\pi}{2} \times 1 + 0 - (0 + 1)[/tex]
[tex] \frac{\pi}{2} + 0 - 1[/tex]
[tex] \frac{\pi}{2} - 1[/tex]
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Ответ:
[tex]\int\limits_{0}^{\frac{\pi}{2}}x \times \cos{x} dx[/tex]
[tex]\int{x \times \cos{x} }dx[/tex]
[tex]u = x \\ dv = \cos{x}dx[/tex]
[tex]du = dx \\ v = \sin{x}[/tex]
[tex]x \times \sin{x} - \int \sin{x}dx[/tex]
[tex]x \times \sin{x} - ( - \cos{x})[/tex]
[tex]x \times \sin{x} + \cos{x}[/tex]
|-ну пусть это предел будет.
[tex](x \times \sin{x} + \cos{x}){|}^{\frac{\pi}{2}}_{0}[/tex]
[tex] \frac{\pi}{2} \times \sin{ \frac{\pi}{2} } + \cos {\frac{\pi}{2} } - (0 \sin{0} + \cos{0})[/tex]
[tex] \frac{\pi}{2} \times 1 + 0 - (0 + 1)[/tex]
[tex] \frac{\pi}{2} + 0 - 1[/tex]
[tex] \frac{\pi}{2} - 1[/tex]