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Multiple Integral Calculator com Passos Explicativos

Gratuito · Privado · Roda no seu navegador — sem necessidade de cadastro

Looking for related tools? Try our integral calculator with steps, our derivative calculator or our limit calculator with steps.

Sem servidor⚡ Web Worker
Definição Exterior Inicial do Processo
∫
d
∫
d
f(x,y) =
Mudança Simbólica de Variáveis / Jacobian
Teclado Matemático
Chargement du clavier…
Exemplos Adicionais.

Estruturas Triviais.

Direcionamento Original Lógico.

  • A Regra da Potência:
    ∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C
  • Constante Básica:
    ∫c dx=cx+C\int c \, dx = cx + C
  • Multiplicador de Constante Interna Analítica e Oficial Resultante Extensivo.:
    ∫cf(x) dx=c∫f(x) dx\int c f(x) \, dx = c \int f(x) \, dx

Funções Categóricas e Extensões Exóticas

  • ∫sin⁡(x) dx=−cos⁡(x)+C\int \sin(x) \, dx = -\cos(x) + C
  • ∫cos⁡(x) dx=sin⁡(x)+C\int \cos(x) \, dx = \sin(x) + C
  • ∫ex dx=ex+C\int e^x \, dx = e^x + C
  • ∫1x dx=ln⁡∣x∣+C\int \frac{1}{x} \, dx = \ln|x| + C
∫∫

Digite a expressão e pressione Ir

Inovando as Integrais Múltiplas Simbólicas

Solucionando variáveis triplas ou matrizes analíticas difíceis rapidamente.

Dupla (2D)

∬Df(x,y) dA\iint_{D} f(x,y) \,dA

Calculate volume under a 3D surface or the area of 2D regions.

Tripla (3D)

∭Ef(x,y,z) dV\iiint_{E} f(x,y,z) \,dV

Calculate total mass, center of mass, and hyper-volumes in 3D space.

Mudança Simbólica de Variáveis

dxdydz=∣J∣ dudvdwdxdydz = |J| \,dudvdw

Automatically map geometries via Jacobian determinants (e.g. Polar).

Como a Integração Funciona

Estando disponível para simulações completas do ambiente de matriz.

Perguntas Frequentes

Lida com derivadas secundárias e terciárias?

Sim! Você pode calcular ordens superiores.

Os resultados são precisos e perfeitos?

O motor algébrico fornece a precisão simbólica exata e confiável.

How do you evaluate a multiple integral step by step?

A multiple integral is evaluated iteratively from the inside out. Integrate with respect to the innermost variable while treating all other variables as constants. Then substitute the inner boundary limits and repeat the integration for each subsequent outer variable.

What is the difference between a double and a triple integral?

A double integral (2D) integrates a function f(x, y) over a planar region to find surface area, 2D mass, or volume under a surface. A triple integral (3D) integrates f(x, y, z) over a 3D solid region to compute total volume, mass distributions, center of mass, and hyper-quantities.

How does Change of Variables work with the Jacobian determinant?

When transforming coordinates (such as from Cartesian (x, y) to Polar (r, θ)), the differential area element is scaled by the absolute value of the Jacobian determinant |J|. For polar coordinates dx dy = r dr dθ.

Does this calculator support Polar, Cylindrical, and Spherical coordinates?

Yes. Mathsway provides built-in coordinate presets for Polar (2D), Cylindrical (3D), and Spherical (3D) transformations with automatic Jacobian determinant evaluation.

Is this multiple integral calculator free and private?

Yes, it is 100% free with no subscription or account required. All computations run in your web browser via Web Workers, keeping your queries completely private.

How are multiple integrals related to derivatives?

Multiple integrals accumulate quantities over multi-dimensional domains, whereas partial derivatives measure rates of change along individual coordinate axes. You can verify antiderivatives with our integral calculator with steps or calculate derivatives with full steps using our derivative calculator.

How do multiple integrals connect to limits and single-variable calculus?

Multiple integrals are Riemann sums taken as partition sizes approach a limit of zero across multiple dimensions. For exploring boundary conditions or single-variable calculus, use our limit calculator with steps.