# Evaluate integral from 0 to 2pi of cos(x)^2 with respect to x

Use the halfangle formula to rewrite as .
Since is constant with respect to , move out of the integral.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Let . Then , so . Rewrite using and .
Let . Find .
Rewrite.
Divide by .
Substitute the lower limit in for in .
Multiply by .
Substitute the upper limit in for in .
Multiply by .
The values found for and will be used to evaluate the definite integral.
Rewrite the problem using , , and the new limits of integration.
Combine and .
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Combine and .
Substitute and simplify.
Evaluate at and at .
Evaluate at and at .
Simplify.
The exact value of is .
Multiply by .
Simplify each term.
Simplify the numerator.
is a full rotation so replace with .
The exact value of is .
Divide by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate integral from 0 to 2pi of cos(x)^2 with respect to x