Calculadora de Integral Dupla (retângulo)

This calculator computes the double integral of a constant function f(x,y)=c over a rectangle defined by the intervals [x1,x2] and [y1,y2]. The result is simply the constant multiplied by the area of the rectangle. For example, for c=5, x1=0, x2=2, y1=1, y2=4, the result is 5*(2-0)*(4-1)=30. The tool is useful for verifying manual calculations or for learning, showing step-by-step application of the formula.

The double integral of a constant function over a rectangular region is an important special case in multivariable calculus. It represents the volume of a rectangular prism with height c and rectangular base. The formula used is ∬_R c dA = c * (x2-x1) * (y2-y1). The calculator automates this calculation, avoiding multiplication errors or typos in the integration limits.

When to use this calculator? In situations where you need to quickly calculate the volume of a solid of constant height over a rectangular base, such as in engineering, physics, or basic math problems. It is also useful for checking exercise results or simulating different constant values and dimensions. Remember that the function must be constant; for non-constant functions, other tools or methods are required.

Cautions: ensure the limits are in the correct order (x1 < x2 and y1 < y2). The calculator does not validate this condition, so input coherent values. Also, the function must be constant; if you enter a variable expression, the result will be incorrect. Use the tool only for its specific purpose of integrating constants over rectangles.