# 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 .

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

Substitute and simplify.

Evaluate at and at .

Raise to the power of .

Combine and .

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 .

Raise to the power of .

Multiply by .

Combine and .

Move the negative in front of the fraction.

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 .

Subtract from .

Multiply and .

Subtract from .

Reduce the expression by cancelling the common factors.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Multiply by .

Simplify.

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Combine using the product rule for radicals.

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form: