Answer
$-\frac{3}{2}cos(\frac{2\theta}{3}) +C$
Work Step by Step
Evaluate the Integral using substitution: $\int sin(\frac{2\theta}{3}) d\theta$
Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$
$u= \frac{2\theta}{3}$
$du =\frac23$
In this expression du is multipled by $\frac32$ to equal $1$
Solve the integral in terms of $u$:
$\int sin(u)(\frac32)du$
$\frac{3}{2}\int sin(u)du $
$-\frac{3}{2}cos(u) +C$
Substitute for $u$:
$-\frac{3}{2}cos(\frac{2\theta}{3}) +C$
