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Calculus Examples
Step 1
Integrate by parts using the formula , where and .
Step 2
Since is constant with respect to , move out of the integral.
Step 3
Step 3.1
Multiply by .
Step 3.2
Multiply by .
Step 4
The integral of with respect to is .
Step 5
Step 5.1
Combine and .
Step 5.2
Substitute and simplify.
Step 5.2.1
Evaluate at and at .
Step 5.2.2
Simplify.
Step 5.2.2.1
Multiply by .
Step 5.2.2.2
Multiply by .
Step 5.2.2.3
Add and .
Step 5.3
Simplify.
Step 5.3.1
The exact value of is .
Step 5.3.2
Multiply by .
Step 5.3.3
Add and .
Step 5.4
Simplify.
Step 5.4.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 5.4.2
The exact value of is .
Step 5.4.3
Multiply by .
Step 5.4.4
Multiply by .
Step 5.4.5
Multiply by .
Step 6
Step 6.1
Simplify each term.
Step 6.1.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 6.1.2
The exact value of is .
Step 6.2
Add and .
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: