# Find the Average Value of the Function f(x)=e^x , [0,5]

,
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
is continuous on .
is continuous
The average value of function over the interval is defined as .
Substitute the actual values into the formula for the average value of a function.
The integral of with respect to is .
Substitute and simplify.
Evaluate at and at .
Simplify.
Anything raised to is .
Multiply by .
Simplify the denominator.
Multiply by .