Sketch the region and find its area.

Question

S = {(x,y) | x > -6, 0 < y < e-x/2}

Answer 1

area = ∫e^(-x/2) dx from x = -6 to ∞
= [-2 e^(-x/2) ] from -6 to ∞
= 0 - (-2e^3)
= 2e^3

note: as x ---> ∞ , e^(-huge) = 1/e^huge ---> 0