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 to get .
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 .
Remove unnecessary parentheses.
Simplify each term.
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of to get .
Divide by to get .
Raising to any positive power yields .
Divide by to get .
Multiply by to get .
Add and to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Subtract from to get .
Add and to get .
Simplify the denominator.
Tap for more steps...
Multiply by to get .
Add and to get .
Multiply by to get .
Enter YOUR Problem

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

Please enter an email address
Please enter a valid email address
The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Mathway Premium

Step-by-step work + explanations
  •    Step-by-step work
  •    Detailed explanations
  •    No advertisements
  •    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month
$--.--/year (--%)

Mathway Premium

Visa and MasterCard security codes are located on the back of card and are typically a separate group of 3 digits to the right of the signature strip.

American Express security codes are 4 digits located on the front of the card and usually towards the right.
This option is required to subscribe.
Go Back

Step-by-step upgrade complete!

Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]