Area Between two Curves Calculator

Area Between two Curves Calculator calculates the area for the given curves and limits. The area under a curve can be determined by performing a definite integral between the given limits.

What is Area Between two Curves Calculator?

Area Between two Curves Calculator is an online tool that helps to calculate the area for the given curves and limits. This online area between two curves calculator helps you to calculate the area between the two curves in a few seconds. To use this area between two curves calculator, enter the function and limit values in the given input box.

How to Use Area Between two Curves Calculator?

Please follow the steps below to find the area using an online area between two curves calculator:

• Step 1: Go to Cuemath’s online area between two curves calculator.
• Step 2: Enter the larger function and smaller function in the given input box of the area between two curves calculator.
• Step 3: Enter the limits(Lower and upper bound) values in the given input box of the area between two curves calculator.
• Step 4: Click on the "Calculate" button to find the area for the given curves and limits.
• Step 5: Click on the "Reset" button to clear the fields and enter the new values.

How Area Between two Curves 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 y = f(x) and y = g(x) be the curves and a and b are two limits. The formula to calculate the area between two curves is given by

\(Area = \int_{a}^{b}[f(x)-g(x)]\)

Let us understand this with the help of the following example.

Solved Example on Area Between two Curves

Find the area for the given curves  f(x) = x² + 2x and g(x) = x + 3 for the interval [1, 3] and verify it using the area between two curves calculator

Solution:

Given: f(x) = x² + 2x and g(x) = x + 3 

\(Area = \int_{a}^{b}[f(x)-g(x)]\)

 \(=\int_{1}^{3}[(x^2 + 2x)-(x+3)]\)

\(=\int_{1}^{3}[(x^2 + x-3)]\)

= 6.67

Similarly, you can try the area between two curves calculator and find the area for:

• f(x) = 5x + 6 and g(x) = 6x² for limits x = -3 to 1
• f(x) = x³ / 2 and g(x) = 5x for limits x = 2 to x = 5

☛ Related Articles:

• Area Under the Curve Calculator
• Integral Calculator