Multivariable Integral Calculator
Calculate definite and indefinite multivariable integrals online. Easily input your function, variables, and limits for step-by-step solutions. Ideal for calculus students and professionals.
Enter the function with variables like x, y, z. Use standard math syntax.
Specify the variable with respect to which you want to integrate.
Enter integration limits as a JSON array [lower, upper] for definite integrals. Leave empty for indefinite integrals.
Result:
Error:
Understanding Multivariable Integrals
Multivariable integrals extend the concept of single-variable integrals to functions of multiple variables. They are used to calculate volumes, areas, and other quantities in higher dimensions.
Definite Integrals: When limits are provided, the calculator computes the definite integral over the specified range for the given variable. For example, integrating with respect to \'x\' from [0, 1] calculates the area under the curve along the x-axis within these limits, considering other variables as constants.
Indefinite Integrals: Without limits, the calculator finds the indefinite integral, which is a function whose derivative with respect to the chosen variable is the original function. This result will include an arbitrary constant of integration, which is omitted in the output for simplicity.
Example: For the function f(x, y) = x*y², integrating with respect to x would treat y as a constant. A definite integral from x=0 to x=2 would give a numerical value, while an indefinite integral would result in a function of x and y.
This tool is powered by math.js for accurate calculations.