# Calculus Examples

,

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.

Since is constant with respect to , move out of the integral.

By the Power Rule, the integral of with respect to is .

Combine and .

By the Power Rule, the integral of with respect to is .

Combine and .

Since is constant with respect to , move out of the integral.

Combine and .

Substitute and simplify.

Evaluate at and at .

Evaluate at and at .

Raise to the power of .

Raise to the power of .

Combine the numerators over the common denominator.

Subtract from .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Raise to the power of .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Raise to the power of .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Combine the numerators over the common denominator.

Subtract from .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Add and .

Subtract from .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Divide by .