# Calculus Examples

Find the Average Value of the Function
,
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.
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.
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Combine fractions.
Write as a fraction with denominator .
Multiply and to get .
Since is constant with respect to , the integral of with respect to is .
Evaluate at and at .
Evaluate at and at .
Remove unnecessary parentheses.
Simplify each term.
Simplify each term.
Raise to the power of to get .
Divide by to get .
Raising to any positive power yields .
Divide by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Subtract from to get .
Simplify the denominator.
Multiply by to get .
Multiply by to get .

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