Question
Sketch the region on paper. If it is a finite region, find its area. Round your answer to three decimal places. (If the area is not finite, enter NONE.)
S = {(x,y) | x ≥ −4, 0 ≤ y ≤ e-x/2}
S = {(x,y) | x ≥ −4, 0 ≤ y ≤ e-x/2}
Answers
Steve
∫[-4,∞] e^-(x/2) dx
= -2 e^(-x/2) [4,∞]
= -2 (e^(-∞) - e^(-2))
= -2 (0 - 1/e^2)
= 2/e^2
= -2 e^(-x/2) [4,∞]
= -2 (e^(-∞) - e^(-2))
= -2 (0 - 1/e^2)
= 2/e^2