∫(0→1) dx ∫(0→1 - x) 12e^[- (3x + 4y)] dy
= ∫(0→1) dx ∫(0→1 - x) 12e^[- (3x + 4y)] (- 1/4)d[- (3x + 4y)]
= - 3∫(0→1) e^[- (3x + 4y)] |(0→1 - x) dx
= - 3∫(0→1) e^[- (3x + 4(1 - x)] - e^[- (3x)] dx
= - 3∫(0→1) e^(x - 4) dx + 3∫(0→1) e^(- 3x) dx
= - 3e^(x - 4) + 3(- 1/3)e^(- 3x) |(0→1)
= [- 3e^(1 - 4) - e^(- 3)] - [- 3e^(- 4) - 1]
= 1 + 3/e⁴ - 4/e³
≈ 0.855799