Reduction Formula for Integral of Power of Sine/Proof 1

Proof
Let $n \ge 2$.

Let:
 * $\displaystyle I_n := \int \sin^n x \ \mathrm d x$

Then:

thus demonstrating the identity for all $n \ge 2$.

When $n = 1$ this degenerates to:

From Primitive of Sine Function this shows that the identity still holds for $n = 1$.