Calculus Examples

,
The Root Mean Square (RMS) of a function over a specified interval is the square root of the arithmetic mean (average) of the squares of the original values.
Substitute the actual values into the formula for the root mean square of a function.
Evaluate the integral.
Tap for more steps...
Let . Then , so . Rewrite using and .
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 .
By the Power Rule, the integral of with respect to is .
Simplify the answer.
Tap for more steps...
Write as a fraction with denominator .
Multiply and .
Write as a fraction with denominator .
Multiply and .
Evaluate at and at .
Raise to the power of .
Raising to any positive power yields .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Factor out of .
Divide by .
Multiply by .
Add and .
Rewrite as a product.
Multiply and .
Multiply by .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify the root mean square formula.
Tap for more steps...
Simplify the expression.
Tap for more steps...
Multiply by .
Multiply and .
Add and .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Factor out of .
Cancel the common factors.
Tap for more steps...
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Simplify the numerator.
Tap for more steps...
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply by .
Simplify.
Tap for more steps...
Combine.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Enter YOUR Problem
Mathway requires javascript and a modern browser.