Determine the area bounded by the curve $y = x^2$, the x-axis, and the vertical lines $x = 0$ and $x = 3$.

Find the area of the region bounded by the line $y = 2x + 3$, the x-axis, and the ordinates $x = 0$ and $x = 2$.

What is the total area under one complete arch of the sine curve, specifically from $x = 0$ to $x = \pi$?

Find the area of the circle x² + y² = a² using the method of integration.

Find the area bounded by the parabola x² = 4y and the line y = 4.