A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional form, it can be written alpha=fdx_1 ^ ... ^ dx_n and so int_Balpha=int_Bfdmu, (1) where the integral is the Lebesgue integral. On a manifold M covered by coordinate charts U_i, there is a partition of unity rho_i such that 1 ...Custom Solutions. Pre-built Wolfram|Alpha APIs. . Use the Full Results API for these advanced features. Suitable for rapid responses, small screens or integration into bots etc. Suitable for delivery either standalone or in combination with text or report delivery. Includes disambiguation, JSON for structured data, length control, etc. and more ...Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. integral. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students ...

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