# 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
Since is constant with respect to , move out of the integral.
Step 6
By the Power Rule, the integral of with respect to is .
Step 7
Step 7.1
Combine and .
Step 7.2
Substitute and simplify.
Step 7.2.1
Evaluate at and at .
Step 7.2.2
Simplify.
Step 7.2.2.1
Raise to the power of .
Step 7.2.2.2
Cancel the common factor of and .
Step 7.2.2.2.1
Factor out of .
Step 7.2.2.2.2
Cancel the common factors.
Step 7.2.2.2.2.1
Factor out of .
Step 7.2.2.2.2.2
Cancel the common factor.
Step 7.2.2.2.2.3
Rewrite the expression.
Step 7.2.2.2.2.4
Divide by .
Step 7.2.2.3
Raising to any positive power yields .
Step 7.2.2.4
Cancel the common factor of and .
Step 7.2.2.4.1
Factor out of .
Step 7.2.2.4.2
Cancel the common factors.
Step 7.2.2.4.2.1
Factor out of .
Step 7.2.2.4.2.2
Cancel the common factor.
Step 7.2.2.4.2.3
Rewrite the expression.
Step 7.2.2.4.2.4
Divide by .
Step 7.2.2.5
Multiply by .
Step 7.2.2.6
Step 7.2.2.7
Multiply by .
Step 8
Simplify the denominator.
Step 8.1
Multiply by .
Step 8.2