Evaluate the definite integrals`int0pi/4sin2xdx`

Explanation

To evaluate the definite integral \(\int_0^{\frac{\pi}{4}} \sin(2x) \, dx\), we will use substitution to simplify the integral.

### Step-by-Step Solution:

1. **Substitution**: Let \( t = 2x \). Then, differentiate both sides to find \( dx \):
\[ dt = 2 \, dx \quad \Rightarrow \quad dx = \frac{dt}{2} \]
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