## Calculus 8th Edition

$-\frac{3}{2}cos(\frac{2\theta}{3}) +C$
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 $u$: $-\frac{3}{2}cos(\frac{2\theta}{3}) +C$