Introduction to Area Between two Curves Calculator:
Area between two curves calculator is an online tool that helps you to evaluate the area under two curves in a coordinate plane region. It is used to compute the area enclosed by two curves over a specified interval in a bounded region.
Our area between curves calculator with steps is useful for everyone because mistakes are common during manual calculations so this tool will ensure accuracy and efficiency in computing the area between curves.
What is Area between Curve?
The area between curves is a process to measure the total area enclosed by two functions over a specified interval. It uses the integration method to find the absolute difference between the functions, where the curves intersect within the interval [a, b].
It is a fundamental concept in calculus that is used in various applications of mathematics, science, and engineering. The formula used by the area between two curves calculator with steps is,
If f(x) ≥ g(x) on [a,b], the area is,
$$ A \;=\; \int_a^b (f(x) - g(x)) dx $$
If g(x)≥f(x) on [a,b] is, the area A is,
$$ A \;=\; \int_a^b (g(x) - f(x)) dx $$
How to Find Area Between two Curves?
To find the area between two curves y = f(x) and y = g(x) over a specified interval [a,b], the area between the curves calculator uses the following steps to easily calculate the area between two curves.
Step 1:
Identify the functions which is above the other on the interval [a, b].
Step 2:
After identifying the function, choose the formula as per the given problem to find the area between two curves such as: If f(x) > g(x) then [a, b].
$$ A \;=\; \int_a^b (f(x) - g(x)) dx $$
If g(x) > f(x) then [a, b],
$$ A \;=\; \int_a^b (g(x) - f(x)) dx $$
Step 3:
After that put the given value of f(x) and g(x) in the above formula. For integration you can use any method. For simple integration use the direct method and for complex function, use integration techniques such as substitution, integration by parts, or partial fractions.
Step 4:
If the curves and the region between line segments intersect, the integral split and sum of absolute values of differences between the curves over each segment for total area consider the absolute value.
Step 5:
After integration, the upper and lower limits of integration a and b into the integral, find the area between the curve as a solution.
Solved Example of Area between Curve:
An example of the area between the curves will give you in-depth knowledge about the calculation process of the area between two curves calculator.
Example:
Calculate the area of region R, if R is the region bounded above the graph of the following function and below by the graph of the function g(x) = 6 - x.
$$ f(x) \;=\; 9 - (\frac{x}{2})^2 $$
Solution:
Setting f(x) = g(x) we would get,
$$ f(x) \;=\; g(x) $$
$$ 9 - (\frac{x}{2})^2 \;=\; 6 - x $$
$$ 9 - \frac{x^2}{4} \;=\; 6 - x $$
$$ 36 - x^2 \;=\; 24 - 4x $$
$$ x^2 - 4x - 12 \;=\; 0 $$
$$ (x - 6)(x + 2) \;=\; 0 $$
Put these values in the formula of the area between the curve,
$$ A \;=\; \int_a^b [f(x) - g(x)] dx $$
$$ =\; \int_{-2}^6 [3 - \frac{x^2}{4} + x] dx $$
$$ =\; \int_{-2}^{6} \left[ 3 - \frac{x^2}{4} + x \right] dx $$
$$ =\; \left[ 3x - \frac{x^3}{12} + \frac{x^2}{2} \right] \biggr|_{-2}^{6} \;=\; \frac{64}{3} $$
Hence the solution of the area between the curve is 64/3.
How to Use Area Between two Curves Calculator?
The area between curves calculator with steps has a simple design that makes it easy for you for evaluating the integral over an interval. Follow our instructions that are given as:
- Choose the variable of integral from the given field to find the area between the curve.
- Enter the integral function to find the area between the curve in the input field.
- Add the upper and lower limits that bound the curve in its field.
- Review the given function before hitting the calculate button to start the evaluation process in the area between the curves calculator.
- Click the “Calculate” button to get the result of your given area between the curve problem.
- If you are trying our area between polar curves calculator for the first time then you can use the load example to learn more about this process.
- Click on the “Recalculate” button to get a new page for finding more solutions of area between the curve problems.
Final Result of Area Between Curves Calculator:
The area between two curves calculator with steps solves the integral function when you give it an input. It gives results as:
- Result Option:
When you click on the result option the area between 2 curves calculator gives you the solution of the integral function problem and find the area between two curves.
- Possible Steps:
When you click on it, this option will provide you the step by step solution of area between the curve.
Advantages of Area Between the Curves Calculator:
The area between three curves calculator gives you many advantages that help you to calculate integral problems and find the area without any trouble. These advantages are:
- The area between two polar curves calculator is a free tool so you can use it for free to find the area between curve problem solutions without spending anything.
- It is an adaptable tool so you can manage various types of integral functions to calculate the area between the curve.
- Our area between 2 curves calculator helps you to get conceptual clarity for the area between the curve process when you use it for practicing.
- It saves the time that you consume in calculation of the integral problems.
- The area between polar curves calculator is a reliable tool that provides you with accurate solutions whenever you use it to calculate the area between the curve question.
- The area between two curves calculator with steps provides the solution without imposing any condition of signup during the evaluation process.
