`int_(0)^(pi/4) sin^(3) x dx=(2)/(3)`

Explanation

To solve the integral \( \int_{0}^{\frac{\pi}{4}} \sin^3 x \, dx \) and show that it equals \( \frac{2}{3} \), we can follow these steps:

### Step 1: Rewrite the integrand
We start by rewriting \( \sin^3 x \) in a more manageable form:
\[ \sin^3 x = \sin^2 x \cdot \sin x = (1 - \cos^2 x) \sin x \]
Thus, we can express the integral as:
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