Calculus Examples

Evaluate the Integral integral from -1 to 1 of |x| with respect to x
Step 1
Split up the integral depending on where is positive and negative.
Step 2
Since is constant with respect to , move out of the integral.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Combine and .
Step 5
By the Power Rule, the integral of with respect to is .
Step 6
Substitute and simplify.
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Step 6.1
Evaluate at and at .
Step 6.2
Evaluate at and at .
Step 6.3
Simplify.
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Step 6.3.1
Raising to any positive power yields .
Step 6.3.2
Cancel the common factor of and .
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Step 6.3.2.1
Factor out of .
Step 6.3.2.2
Cancel the common factors.
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Step 6.3.2.2.1
Factor out of .
Step 6.3.2.2.2
Cancel the common factor.
Step 6.3.2.2.3
Rewrite the expression.
Step 6.3.2.2.4
Divide by .
Step 6.3.3
Raise to the power of .
Step 6.3.4
Subtract from .
Step 6.3.5
Multiply by .
Step 6.3.6
Multiply by .
Step 6.3.7
One to any power is one.
Step 6.3.8
Multiply by .
Step 6.3.9
Raising to any positive power yields .
Step 6.3.10
Multiply by .
Step 6.3.11
Multiply by .
Step 6.3.12
Add and .
Step 6.3.13
Combine the numerators over the common denominator.
Step 6.3.14
Add and .
Step 6.3.15
Cancel the common factor of .
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Step 6.3.15.1
Cancel the common factor.
Step 6.3.15.2
Rewrite the expression.
Step 7