# Calculus Examples

,
Step 1
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:
Step 2
is continuous on .
is continuous
Step 3
The average value of function over the interval is defined as .
Step 4
Substitute the actual values into the formula for the average value of a function.
Step 5
Split the single integral into multiple integrals.
Step 6
Since is constant with respect to , move out of the integral.
Step 7
By the Power Rule, the integral of with respect to is .
Step 8
Combine and .
Step 9
Apply the constant rule.
Step 10
Substitute and simplify.
Step 10.1
Evaluate at and at .
Step 10.2
Evaluate at and at .
Step 10.3
Simplify.
Step 10.3.1
Raise to the power of .
Step 10.3.2
Raising to any positive power yields .
Step 10.3.3
Cancel the common factor of and .
Step 10.3.3.1
Factor out of .
Step 10.3.3.2
Cancel the common factors.
Step 10.3.3.2.1
Factor out of .
Step 10.3.3.2.2
Cancel the common factor.
Step 10.3.3.2.3
Rewrite the expression.
Step 10.3.3.2.4
Divide by .
Step 10.3.4
Multiply by .
Step 10.3.5
Step 10.3.6
Combine and .
Step 10.3.7
Multiply by .
Step 10.3.8
Cancel the common factor of and .
Step 10.3.8.1
Factor out of .
Step 10.3.8.2
Cancel the common factors.
Step 10.3.8.2.1
Factor out of .
Step 10.3.8.2.2
Cancel the common factor.
Step 10.3.8.2.3
Rewrite the expression.
Step 10.3.8.2.4
Divide by .
Step 10.3.9
Multiply by .
Step 10.3.10
Multiply by .
Step 10.3.11
Step 10.3.12
Subtract from .
Step 11
Simplify the denominator.
Step 11.1
Multiply by .
Step 11.2