# Find the Average Value of the Function f(x)=x^2-13 , [0, square root of 26]

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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.
By the Power Rule, the integral of with respect to is .
Since is constant with respect to , move out of the integral.
Combine and .
Substitute and simplify.
Evaluate at and at .
Simplify.
Rewrite as .
Raise to the power of .
Combine and .
Raising to any positive power yields .
Multiply by .
Multiply by .
Multiply by .
Simplify.
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Simplify the denominator.
Multiply by .
Reduce the expression by cancelling the common factors.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Find the Average Value of the Function f(x)=x^2-13 , [0, square root of 26]

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