Average value of f(x) = e ^ 4xsquared on the interval [-1/4,1/4]

Answer 1

f(x) = e^(4x^2)

f(-1/4) = e^(1/4)
f(1/4) = e^(1/4)

avg value = (e^(1/4) - e^(1/4) )/(1/2)
= 0

Answer 2

Hmmm. As I recall, the average value of f(x) on [a,b] is

∫[a,b] f(x) dx
------------------
b-a

e^(4x^2) is an even function, so its average value cannot be zero over [-1/4,1/4].

∫[-1/4,1/4] e^(4x^2) dx

Unfortunately, ∫e^(x^2) dx is not an elementary integral.

Answer 3

Steve , you are right,
I read the question rather superficially.

(notice it was my last post last night, must have been a bit tired)