Calculus Examples

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Step 1
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.
Step 2
Substitute the actual values into the formula for the root mean square of a function.
Step 3
Evaluate the integral.
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Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Multiply by .
By the Power Rule, the integral of with respect to is .
Substitute and simplify.
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Evaluate at and at .
Simplify.
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Raise to the power of .
Combine and .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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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 .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Step 4
Simplify the root mean square formula.
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Multiply by .
Subtract from .
Reduce the expression by cancelling the common factors.
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Multiply by .
Combine and simplify the denominator.
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Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Simplify the numerator.
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Combine using the product rule for radicals.
Multiply by .
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Step 6
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