What is the integral of-cos(2θ) ?

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

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integral of-cos(2θ)

\int - cos (2 θ) d θ

- \frac{1}{2} sin (2 θ) + C

Solution steps

\int - cos (2 θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int cos (2 θ) d θ

Apply u-substitution

: \int cos (u) \frac{1}{2} d u

= - \int cos (u) \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= - \frac{1}{2} sin (u)

Substitute back

u = 2 θ

= - \frac{1}{2} sin (2 θ)

Add a constant to the solution

= - \frac{1}{2} sin (2 θ) + C

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