Area Under the Curve Formula

Area Under Normal Curve Formula

The area under a curve between two points is identified by conducting a definite integral between the two points. In order to calculate the area under the curve y = f(x) between x = a & x = b, integrate y = f(x) between the limits of a and b. This area can be simply identified with the help of integration using given limits.


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Formula to Calculate the Area Under a Curve

Area of curve formula = \[\int_{a}^{b} f(x)dx\]


Formula For Area Between Two Curves

The basic formula used to calculate the area between two curves is as below:

If P: y = f(x) and

 Q: y = g(x) and

x1 and x2 are the two limits, and then the formula for area between two curves is,

Area between Two Curves; \[A = \int_{x_{2}}^{x_{1}} [f(x) - g(x)]\]


Calculating Area Under Curve

You will have the accessibility of an online free tool that can be used to calculate area between two curves. The area between two curves calculator is available at Vedantu official which easily provides the area occupied within two curves. This area between two curves calculators online helps students easily find areas under curve excel, make the calculations faster, and it displays the final answer in the blink of an eye. The online tool can also be used as an area under curve calculator with rectangles. Having said that, let’s see how to use the curve calculator.


How to Use the Area Between Two Curves Calculator?

Follow the step-by-step procedure to use the area between the two curves calculator and get your right answer in fraction of seconds.

Step 1: First insert the smaller function, then the larger function and finally the limit values in the provided input fields

Step 2: Click the button “Calculate Area” to obtain the resultant

Step 3: Ultimately, the area between two curves will be shown in the new window.


Solved Example

Example: Find out the area under the curve of a function, f(x) = 7 – x², the limit is provided as x = -1 to 2.

Solution:

Given is the function; f(x) = 7- x² and

Limit is x = -1 to 2

Now, for calculating area under curve we will use the formula i.e. ∫ab f(x)dx

Plugging in the values, we have

Area = \[\int_{-1} ^{2} (7 - x^{2})dx\]

= \[(7x - 13x^{3}) |^{2}_{−1}\]

= {7.2−13 (8)} − {7(−1} −13 (−1)}

= {(42 – 8)/3} – {(1 – 21)/3}

= (34 + 20)/3

= 54/3

= 18 sq.units

FAQs (Frequently Asked Questions)

1. What is the Area Between Two Curves?

Answer: The area between the two curves is described as the total region occupied between the two curves in the coordinate plane system.

2. How Do We Calculate The Area Between Two Curves?

Answer: The area between two curves can be computed by taking absolute difference of the definite integrals between the two functions. In 2-D geometry, the area is a quantity which depicts the region occupied by the two-dimensional figure. Two functions are needed to identify the area, say f(x) and g(x), and the integral limits from a to b (b should be higher than a) of the function, which illustrates the curve.

3. Can The Area Between The Two Curves Be Negative?

Answer: When both the curves lie under the x-axis, then the area between two curves is negative. However, the net signed value will be considered as the final answer.