# Find the Average Value of the Function f(x)=16-x^2 , [-4,4]

,
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.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Combine and .
Substitute and simplify.
Evaluate at and at .
Evaluate at and at .
Simplify.
Multiply by .
Multiply by .
Raise to the power of .
Raise to the power of .
Move the negative in front of the fraction.
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the Average Value of the Function f(x)=16-x^2 , [-4,4]

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