Question

The average value of a even function is a) +ve b) -ve c) infinite d) none. which option is correct and why?

Answer 1

Answer:

The average value of a function, or the average height of a function, is the height of the rectangle that has area equivalent to the area under the curve of the function. It is defined generally by the equation. 1(b−a)∫baf(x)dx.

Answer 2

Given : even function

To find : Average value of function

Solution:

The average value of a even function   will depend upon  Domain  & range

for an even function average from -a to 0  or 0 to a   or  -a to a  is  same

f(x) =  x²   then average value is + ve

f(x) = - x²  then average value is - ve

Hence none   option is correct

But average value of an odd function  =  0

for symmetric domain

because in odd function  f(x) = -f(-x)

hence from domain -a  to a  , sum of range = 0

hence average  = 0   for odd function

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