Double Integral Calculator
Compute double integrals over rectangular regions with step-by-step explanation.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator approximates a double integral using the midpoint rule with 100 subintervals per dimension. Follow these steps:
- Enter Inner Limits (for y): Provide the lower limit (a) and upper limit (b) for the inner integral (integrated with respect to y).
- Enter Outer Limits (for x): Provide the lower limit (c) and upper limit (d) for the outer integral (integrated with respect to x).
- Enter the Integrand f(x,y): Type the function using
xandyas variables (e.g.,x*y,sin(x+y),x^2 + y^2). Use standard JavaScript syntax (e.g.,Math.sinfor sine). - Click "Calculate": The result appears as a decimal number, along with a brief explanation of the method used.
Important: All limits must be numbers, and the inner lower limit must be less than the inner upper limit (same for outer limits). The calculator uses the midpoint rule—results are approximations, not exact symbolic values.
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Frequently Asked Questions
A double integral computes the volume under a surface f(x,y) over a region in the xy-plane.
The calculator uses the midpoint rule with 100 subintervals per dimension for numerical approximation.
Use JavaScript syntax: e.g., x*y for x times y, Math.sin(x) for sine, Math.exp(x*y) for exponential.
