Задача 71059 ...

64358bfbbec86814fb6ff6fb

27.04.2023 12:37:11

Найти F′(y)

F(y) = ∫ e^(-yx^2) dx

5f3ea7e3faf909182968ddd9

27.04.2023 17:35:54

★

Ф`(y)=[m] ∫^{y^2} _{y}(e^{-yx^2})`_{y}dx+e^{-y\cdot(y^2)^2}\cdot (y^2)`_{y}-e^{-y\cdot(y)^2}\cdot (y)`_{y}=[/m]

[m]=∫^{y^2} _{y}e^{-yx^2}\cdot (-x^2)dx+e^{-y\cdot(y^2)^2}\cdot (y^2)`_{y}-e^{-y\cdot(y)^2}\cdot (y)`_{y}=[/m]


[m]=∫^{y^2} _{y}e^{-yx^2}\cdot (-x^2)dx+2y\cdot e^{-y^5}-e^{-y^3}=[/m]

интеграл считаем по частям:

[m]u=x[/m]

[m]dv=e^{-yx^2}\cdot x dx[/m]