Area Between Curves Calculator
Calculate the area between two functions using numerical integration.
Results
Area
1.5 square units
Calculation Steps
Find Intersection Points
Formula: f₁(x) = f₂(x)
Result: 0
Calculate Area
Formula: ∫[f₁(x) - f₂(x)]dx
Result: 1.5003333333333333
Recommendations
Accuracy
Current interval count provides good accuracy
Integration Method
Simpson's Rule provides good balance of accuracy and speed
Domain
No intersection points in given domain
Verification
Cross-check result with graphical representation
Understanding Area Between Curves
The area between two curves is calculated by finding the definite integral of the difference between the upper and lower functions over a specified interval.
Key Concepts
- • Definite integration
- • Function intersection points
- • Numerical methods
- • Interval selection
Common Applications
- • Physics problems
- • Engineering analysis
- • Economic modeling
- • Statistical analysis
Integration Methods
Simpson's Rule
A numerical integration method that approximates the definite integral by using quadratic polynomials to estimate the area.
Trapezoidal Rule
A simpler method that approximates the area using trapezoids. Less accurate but faster than Simpson's Rule.
Tips for Accurate Results
Function Input
- • Use standard mathematical notation
- • Check for valid expressions
- • Verify function domains
Interval Selection
- • Check for intersections
- • Consider function behavior
- • Verify endpoint values
Verification
- • Compare with graphs
- • Check reasonableness
- • Validate assumptions