Find the area under the curve y=6xe−x y = 6 x e − x for x≥2 x ≥ 2 . area =

Answer 1

Area A = ∫₂^∞6xe^-xdx =

We do integration by parts: u = 6x du = 6, dv = e^-xdx, v = - e^-x.

Then A = - 6xe^(-x)₂∞ ^{+ ∫}₂^∞e^(-x)dx =12e^-2 - 6e^-x₂^∞ = 12e^-2 + 6e^-2 = 18/e² ≈ 2.436