Wat is f (x) = int xe ^ x als f (2) = 3?

Wat is f (x) = int xe ^ x als f (2) = 3?
Anonim

Antwoord:

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

Uitleg:

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

we gebruiken integratie door delen

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

in dit geval

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

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

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

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

# f (2) = 3 #

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

# C = 3-e ^ 2 #

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