integral of sin(2θ) — step-by-step solution

⚠ 2θ is read as the product 2*θ: for a power, write 2^θ

Let's compute the integral:

\int(\sin (2 θ))dθ

To use the known integral of

\sin (u)

, let

u = 2 θ

. Then

du = 2 dθ

, so

dθ = \frac{1}{2} \cdot du

We use

\int(\sin (u))du = - \cos (u)

, then substitute

u = 2 θ

back

- \frac{\cos (2 θ)}{2}

▶Indefinite integrals are defined up to an additive constant C, so this yields:

- \frac{\cos (2 θ)}{2} + C