,

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 .

Add and .

Multiply by .

Add and .

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.

Multiply by .

Add and .

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]