Parabolas are fascinating geometric structures. They possess a unique property: every point on a parabola is equidistant from a special point called the center. This attribute gives rise to the classic appearance of a parabola, often characterized as a balanced curve that extends either downwards. In geometry, parabolas have various applications.

In calculus, determining the area under a parabola represents a fundamental concept. This region is limited by the parabola's curve, the x-axis, and two specific vertical lines representing the boundaries of integration. To find this area, we employ the definite integral, which provides a precise measurement of the area under the curve. The result