# Calculus Examples

Find the Average Value of the Equation
,
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 .
Since is constant with respect to , the integral of with respect to is .
Evaluate at and at .
Evaluate at and at .
Raise to the power of .
One to any power is one.
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Multiply by .
Multiply by .