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Try an Example
Pick a scenario to see how the calculator works, then adjust the values
Basic Polynomial
Integrate x^2 from 0 to 1 using Simpson's rule. Exact answer: 1/3.
Key values: x^2 · [0, 1] · Simpson's rule
Trigonometric Integral
Integrate sin(x) from 0 to pi. Exact answer: 2.
Key values: sin(x) · [0, pi] · Exact: 2
Area Under a Bell Curve
Approximate the Gaussian integral e^(-x^2) from -3 to 3.
Key values: e^(-x^2) · [-3, 3] · Gaussian
This calculator is also known as Area Calculator (Calculus).
Read the complete guideGeometry vs Calculus for Area
Geometric formulas work for rectangles, triangles, and circles. Calculus extends area calculation to any curve. The definite integral gives the signed area; the integral of |f(x)| gives the total area.
Examples
Area of a Parabolic Region
Find the area under y = x^2 from 0 to 3.
The antiderivative is x^3/3. Area = 27/3 - 0 = 9 square units.
Key takeaway: Integration handles curved boundaries that geometry formulas cannot.
Understanding Area via Integration
Build your understanding of calculus-based area:
- Start with areas you can verify geometrically (rectangles, triangles)
- Observe how the signed area differs from the total area for oscillating functions
- Use the Riemann sum slider to see how rectangles approximate the area
Frequently Asked Questions about Area Calculator (Calculus)
What is the difference between signed area and total area?
Signed area counts regions below the x-axis as negative, so they subtract from the total. Total area uses |f(x)| so all regions contribute positively. For sin(x) from 0 to 2pi, signed area = 0 but total area = 4.
Specialized Calculators
Choose from 7 specialized versions of this calculator, each optimized for specific use cases and calculation methods.
Purpose
3 CalculatorsMethod
4 CalculatorsAlternative methods and approaches
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