Area Between Curves Calculator
Calculate the area between two curves with step-by-step solutions
Results
About Area Between Curves
The area between two curves f(x) and g(x) from x = a to x = b is calculated using the definite integral:
This calculator assumes f(x) ≥ g(x) in the given interval. If the curves intersect within the interval, you may need to split the calculation at intersection points.
The area between curves calculator is a mathematical tool used to find the region enclosed by two functions within a specified interval. This calculation is an important concept in calculus, particularly in definite integration. The area is determined by integrating the difference between the upper and lower functions across the given bounds. This calculator provides both numerical results and visual representation of the area, making it easier to understand the geometric interpretation of the integral.
How to Calculate the Area Between Two Curves
Step 1: Enter the Upper and Lower Functions
Input the upper function f(x) and lower function g(x) in the designated fields. Use standard mathematical notation (e.g., x^2 for x², sqrt(x) for √x, sin(x) for sine). Make sure the upper function is greater than or equal to the lower function throughout the interval.
Step 2: Specify the Integration Bounds
Enter the lower and upper bounds for the integration. These values define the interval [a,b] over which the area will be calculated. You can use numerical values or mathematical expressions (e.g., pi/2, sqrt(2)).
Step 3: Select Calculation Options
Check the “Show calculation steps” box if you want to see the detailed solution process. This is particularly useful for educational purposes or to verify your manual calculations.
Step 4: Calculate and Interpret Results
Click the “Calculate Area” button to process your input. The calculator will display the numerical result of the area, a graphical representation showing the region between the curves, and (if selected) the step-by-step calculation process.
Step 5: Analyze the Visual Representation
Examine the generated graph to visualize the area between the curves. The shaded region represents the calculated area. You can hover over different points on the graph to see the exact function values at those points.