Question
Calculate the area under the graph of y = e^–x above the x-axis for the interval [1, ∞].
a) 0
b) e^-1
c) -e^-1
d) infinity
a) 0
b) e^-1
c) -e^-1
d) infinity
Answers
Reiny
∫ e^-x dx from 1 to ∞
= [ -e^-x] from 1 to ∞
= [ -1/e^x] from 1 to ∞
= -1/e^∞ - (-1/e^1)
= 0 + 1/e
= 1/e
confirmation: www.wolframalpha.com/input/?i=%E2%88%AB+e%5E-x+dx+from+1+to+%E2%88%9E
= [ -e^-x] from 1 to ∞
= [ -1/e^x] from 1 to ∞
= -1/e^∞ - (-1/e^1)
= 0 + 1/e
= 1/e
confirmation: www.wolframalpha.com/input/?i=%E2%88%AB+e%5E-x+dx+from+1+to+%E2%88%9E