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Calculus Examples
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Step 2.1
Let . Find .
Step 2.1.1
Differentiate .
Step 2.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 2.1.3
Differentiate using the Power Rule which states that is where .
Step 2.1.4
Multiply by .
Step 2.2
Substitute the lower limit in for in .
Step 2.3
Multiply by .
Step 2.4
Substitute the upper limit in for in .
Step 2.5
Cancel the common factor of .
Step 2.5.1
Factor out of .
Step 2.5.2
Cancel the common factor.
Step 2.5.3
Rewrite the expression.
Step 2.6
The values found for and will be used to evaluate the definite integral.
Step 2.7
Rewrite the problem using , , and the new limits of integration.
Step 3
Combine and .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Step 5.1
Combine and .
Step 5.2
Cancel the common factor of and .
Step 5.2.1
Factor out of .
Step 5.2.2
Cancel the common factors.
Step 5.2.2.1
Factor out of .
Step 5.2.2.2
Cancel the common factor.
Step 5.2.2.3
Rewrite the expression.
Step 5.2.2.4
Divide by .
Step 6
The integral of with respect to is .
Step 7
Evaluate at and at .
Step 8
Step 8.1
The exact value of is .
Step 8.2
The exact value of is .
Step 8.3
Multiply by .
Step 8.4
Add and .
Step 8.5
Multiply by .