Area Under the Curve Calculator
Area Under the Curve Calculator calculates the area under the curve for the given function. The area under a curve can be determined by performing a definite integral between the given limits.
What is Area Under the Curve Calculator?
Area Under the Curve Calculator is an online tool that helps to calculate the area under the curve for the given function and limits. This online area under the curve calculator helps you to calculate the area under the curve in a few seconds. To use this area under the curve calculator, enter the function and limit values in the given input box.
How to Use Area Under the Curve Calculator?
Please follow the steps below to find the area using an online area under the curve calculator:
- Step 1: Go to Cuemath’s online area under the curve calculator.
- Step 2: Enter the function and limits values in the given input box of the area under the curve calculator.
- Step 3: Click on the "Calculate" button to find the area under the curve for the given function.
- Step 4: Click on the "Reset" button to clear the fields and enter a new function and new limits values.
How Area Under the Curve Calculator Works?
The fundamental theorem of calculus tells us that to calculate the area under a curve y = f(x) from x = a to x = b. It is represented as \(\int\limits_a^b {f\left( x \right)dx}\)
We first calculate the integration g(x) of f(x), \(g\left( x \right)= \int {f\left( x \right)dx}\) and then evaluate g(b) − g(a). That is, the area under the curve f(x) from x = a to x = b is \(\int\limits_a^b {f\left( x \right)dx = g\left( b \right) - g\left( a \right)}\)
Let us understand this with the help of the following example.
Solved Example on Area Under the Curve
Find the area under the curve for the given function \(\int\limits_2^3 {(x + 3)\,dx}\) and verify it using the area under the curve calculator
Solution:
\(= \int\limits_2^3 {x dx} + \int\limits_2^3 {3dx}\)
\(= \frac{x^2}{2}]_2^3 + 3 x]_2^3\)
\(=\frac{1}{2} ( 3^2 - 2^2) + 3(3 - 2)\)
= \(\frac{1}{2}(5) + 3\)
\(=\frac{11}{2}\)
Therefore, area under the curve for the given function is 11 / 2.
Similarly, you can try the area under the curve calculator and find the area for:
- f(x) = 5x + 6 for limits x = -3 to 1
- f(x) = x3 / 2 for limits x = 2 to x = 5