Sketch the region lying in the first quadrant and bounded by `y = 4x^2` ,x = 0, y = 2 and y = 4. Find the area of the region using integration.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Sketch the Region
We need to sketch the region bounded by the curves and lines given:
- The parabola \( y = 4x^2 \)
- The vertical line \( x = 0 \) (y-axis)
- The horizontal lines \( y = 2 \) and \( y = 4 \)

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