Calculus Examples

Evaluate the Integral integral of (1-cos(2x))/2 with respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Split the single integral into multiple integrals.
Step 3
Apply the constant rule.
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Let . Then , so . Rewrite using and .
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Step 5.1
Let . Find .
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Step 5.1.1
Differentiate .
Step 5.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 5.1.3
Differentiate using the Power Rule which states that is where .
Step 5.1.4
Multiply by .
Step 5.2
Rewrite the problem using and .
Step 6
Combine and .
Step 7
Since is constant with respect to , move out of the integral.
Step 8
The integral of with respect to is .
Step 9
Simplify.
Step 10
Replace all occurrences of with .
Step 11
Simplify.
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Step 11.1
Combine and .
Step 11.2
Apply the distributive property.
Step 11.3
Combine and .
Step 11.4
Multiply .
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Step 11.4.1
Multiply by .
Step 11.4.2
Multiply by .
Step 12
Reorder terms.