Calculus Examples

Find the Average Value of the Function
,
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.
Tap for more steps...
Write as a fraction with denominator .
Multiply and .
Since is constant with respect to , the integral of with respect to is .
Simplify the answer.
Tap for more steps...
Evaluate at and at .
Evaluate at and at .
Raise to the power of .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Raising to any positive power yields .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Add and .
Multiply by .
Multiply by .
Multiply by .
Add and .
Subtract from .
Simplify the denominator.
Tap for more steps...
Multiply by .
Add and .
Multiply by .
Enter YOUR Problem
Mathway requires javascript and a modern browser.