# Calculus Examples

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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.

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Multiply by to get .

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

Simplify the answer.

Write as a fraction with denominator .

Multiply and to get .

Evaluate at and at .

Raise to the power of to get .

Raising to any positive power yields .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by to get .

Multiply by to get .

Reorder terms.

Simplify the expression.

Multiply by to get .

Multiply and to get .

Simplify the expression.

Multiply by to get .

Add and to get .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Simplify the numerator.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and to get .

Rewrite as .