The AVERAGE Value of f(x)=e^-x is?

Question

The interval is [0, ln1/2]

a) 1/ln3

b) 1/ln4

c) 1/ln2

d) -1/ln2

e) none of these

P.S I can't understand how to get it.

Answer 1

to find the averge to need to find the area under the curve in the region and devide by length

area = int e^-x = -e^-x

at x = 0 it is -1 and at ln 1/2 it is -e^-(ln 1/2) = -1/2

so area = -1 +1/2 = -1/2

LENGTH =  ln 1/2

so average = -1/2 ln 1/2 or 1/ln 4

so ans is b