Double Integral Calculator
A double integral calculator helps compute the volume under a surface in three-dimensional space. It's essential in physics for calculating moments of inertia, in probability for joint distributions, and in engineering for stress analysis. This tool simplifies complex mathematical operations, saving time and reducing calculation errors for students, researchers, and professionals working with multivariable calculus.
Double Integral Formula
The double integral formula is expressed as:
∬R f(x,y) dA = ∫ab ∫cd f(x,y) dx dy
Where R is the rectangular region [a,b] × [c,d], and dA represents the differential area element.
How to Use
1. Enter your function using standard mathematical notation (e.g., x^2 + sin(y))
2. Input numerical limits for both x and y variables
3. Click Calculate to see the numerical approximation
4. Use Clear to reset all fields
The calculator uses Riemann sum approximation with fixed intervals for quick computation.
Derivation Process
The calculator uses numerical integration through Riemann sums. It divides the area into small rectangles, computes function values at sample points, and sums them multiplied by rectangle areas. The implementation iterates over both x and y directions, accumulating the total sum. Accuracy depends on the fixed interval size (0.01 in this implementation), with smaller intervals providing better precision but requiring more computations.