How to Calculate Area Under a Curve in Integral Calculus

Calculating the area under a curve is an important part of integral calculus. This is done by finding the definite integral of an integrable function and evaluating it at each point on the graph. The definite integral gives you the area under the curve, which is also known as the area of the region.

The area under the curve can be calculated in Cartesian coordinates with rectangular ( x, y) axes and in polar coordinates with a cylinder. It is also possible to calculate the area under a curve by using two-dimensional arrays.

Know Its Equation and the Boundaries

To calculate the area under a curve, you first need to know its equation and the boundaries of the curve and the axis enclosing it. You can do this by figuring out the formula of the curve and analyzing its properties. You can then calculate the area under a curve by integrating with respect to the x-axis and evaluating this at each of the limits. This is a common method of calculating the area under a curve, as the function often maps to a single value of x.

Dividing the Curve Into a Few Rectangles

The area under the curve can also be determined using a different method that involves dividing the curve into a few rectangles and adding the areas of these rectangles together. This is a quick and easy way to get an approximate idea of the area under the curve, but it may not be accurate. If you are having trouble calculating the area under a curve, try the following techniques:

  1. Use a number of subintervals to approximate it. Choosing the number of subintervals is the easiest part of calculating the area under a curve. You can even find this information on the chart that you are working with, such as a velocity time graph.
  2. If you are not sure of the number of subintervals, try a simple method to estimate it by dividing the curve into smaller sections and then estimating each section.
  3. If you do not have access to the data you want to work with, you can also map your data to a trendline and then calculate the area under that curve.
  4. If you are not familiar with the function f(x)=2x+8x, you can also use the definite integral to find it. This is a useful technique for finding the area under a curve, but it can be hard to do if you don’t know the equation of the function or the values of x and y.
  5. If you are not confident in your calculation skills, you can try the online area under the curve calculator tool. It will make the calculation faster and more accurate.


There are different methods for calculating the area under a curve, and the most popular is the antiderivative method of determining it. You can find the area 51 under a curve in a variety of ways, such as by drawing a line between two points, by integrating the function, or by using an antiderivative formula.


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