Was ist f (x) = int xe ^ x wenn f (2) = 3?

Antworten:

#f (x) = xe ^ x-e ^ x + 3-e ^ 2 #

Erläuterung:

#f (x) = intxe ^ xdx, f (2) = 3 #

Wir verwenden die Integration von Teilen

#f (x) = intu (dv) / (dx) dx = uv-intv (du) / (dx) dx #

in diesem Fall

# u = x => (du) / (dx) = 1 #

# (dv) / (dx) = e ^ x => v = e ^ x #

#:. f (x) = xe ^ x-inte ^ xdx #

#f (x) = xe ^ x-e ^ x + c #

# f (2) = 3 #

#:. f (2) = 3 = 2e ^ 2-e ^ 2 + c #

# c = 3-e ^ 2 #

#f (x) = xe ^ x-e ^ x + 3-e ^ 2 #