# 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.

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 .

Write as a fraction with denominator .

Multiply and .

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

Write as a fraction with denominator .

Multiply and .

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

Combine and .

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 .