What is the integral of 1-cos(2θ) ?

The integral of 1-cos(2θ) is θ-1/2 sin(2θ)+C

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integral of 1-cos(2θ)

\int 1 - cos (2 θ) d θ

θ - \frac{1}{2} sin (2 θ) + C

Solution steps

\int 1 - cos (2 θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d θ - \int cos (2 θ) d θ

\int 1 d θ = θ

\int cos (2 θ) d θ = \frac{1}{2} sin (2 θ)

= θ - \frac{1}{2} sin (2 θ)

Add a constant to the solution

= θ - \frac{1}{2} sin (2 θ) + C

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What is the integral of 1-cos(2θ) ?
The integral of 1-cos(2θ) is θ-1/2 sin(2θ)+C