The area under the curve means the area bounded by the curve, the axis, and the boundary points. The area under the curve is a two-dimensional area, which has been calculated with the help of the coordinate axes and by using the integration formula. What Does Area Under the Curve Represent?
Area with respect to the y-axis: The area of the curve bounded by the curve x = f (y), the y-axis, across the lines y = a and y = b is given by the following below expression. Further, the area between the curve and the y-axis can be understood from the below graph.
What Is Area Under the Curve in Velocity Time Graph? In the velocity-time graph, the velocity is graphed with respect to the y-axis, and the time is taken on the x-axis. With this, the area is assumed to be the product of velocity and time and it gives the distance covered.
Therefore the area of the ellipse is πab sq units. The area between a curve and a line can be conveniently calculated by taking the difference of the areas of one curve and the area under the line. Here the boundary with respect to the axis for both the curve and the line is the same.
The area under the curve means the area bounded by the curve, the axis, and the boundary points. The area under the curve is a two-dimensional area, which has been calculated with the help of the coordinate axes and by using the integration formula.
The area of the circle is calculated by first calculating the area of the part of the circle in the first quadrant. Here the equation of the circle x 2 + y 2 = a 2 is changed to an equation of a curve as y = √ (a 2 - x 2 ). This equation of the curve is used to find the area with respect to the x-axis and the limits from 0 to a.
The area under the curve is defined as the region bounded by the function we’re working with, vertical lines representing the function’s bounds, and the $\boldsymbol {x}$ -axis.
When calculating the area under the curve of $f (x)$, use the steps below as a guide: