Double Integral Calculator

Double Integral Formula:

\[ \iint f(x,y) \,dx \,dy \]

Double Integral Result:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Double Integral?

A double integral is an integral over a two-dimensional area that calculates the volume under a surface defined by a function f(x,y) over a region R in the xy-plane. It's represented as ∬f(x,y)dxdy.

2. How Does the Calculator Work?

The calculator computes the double integral using numerical methods:

\[ \iint\limits_{R} f(x,y) \,dA = \int_{a}^{b} \left( \int_{c}^{d} f(x,y) \,dy \right) dx \]

Where:

\( f(x,y) \) — The function to integrate
\( [a,b] \) — x-axis integration limits
\( [c,d] \) — y-axis integration limits

3. Applications of Double Integrals

Details: Double integrals are used to calculate volumes, average values, center of mass, moment of inertia, and probability distributions in two dimensions.

4. Using the Calculator

Tips: Enter the function using standard mathematical notation (e.g., "x^2 + y^2" or "sin(x)*cos(y)"). Specify the rectangular region of integration with lower and upper limits for both x and y.

5. Frequently Asked Questions (FAQ)

Q1: What functions can be integrated?
A: The calculator can handle most continuous functions of two variables, including polynomials, trigonometric, exponential, and logarithmic functions.

Q2: How accurate are the results?
A: Accuracy depends on the numerical method used. More complex functions may require more computation for precise results.

Q3: Can I integrate over non-rectangular regions?
A: This calculator currently supports rectangular regions only. For other shapes, you would need to adjust the limits accordingly.

Q4: What if my integral doesn't converge?
A: The calculator will indicate if the integral appears to be divergent or if the computation exceeds reasonable limits.

Q5: Can I save my calculations?
A: Currently, results are not saved between sessions. You would need to note them down manually.