{ "definitions": { "\\mathbb{R}": [ { "Q12916": "real number (quantity along a continuous line)" } ], "n": [ { "Q4440864": "dimension (minimum number of coordinates within a space needed to specify any point)" } ], "f": [ "integrable function", {} ], "x": [ "variable", {} ], "B": [ { "Q838611": "ball (in mathematics, space inside a sphere)" } ], "x_{0}": [ { "Q44946": "point (fundamental object of Euclidean geometry)" } ], "r": [ { "Q173817": "radius (segment in a circle and its length)" } ], "S": [ "surface", {} ] }, "constraints": [], "math_inputtex": "\\int_{\\mathbb{R}^n}f\\,dx = \\int_0^\\infty\\left\\{\\int_{\\partial B(x_0;r)} f\\,dS\\right\\}\\,dr.", "math_inputtex_semantic": "\\int_{\\w{Q12916}{\\mathbb{R}}^{\\w{Q4440864}{n}}} \\wf{Q853831}{f} \\,d \\w{Q50701}{x} = \\int_0^\\infty\\left\\{\\int_{\\partial \\wf{Q838611}{B}(\\w{Q44946}{x_0}; \\w{Q173817}{r})} f\\,d \\w{Q484298}{S} \\right\\}\\,dr", "correct_tex": "\\int_{\\mathbb{R}^n}f\\,dx = \\int_0^\\infty\\left\\{\\int_{\\partial B(x_0;r)} f\\,dS\\right\\}\\,dr", "correct_mml": "\n \n \n \n \n ∫\n \n ℝ\n n\n \n \n \n \n f\n \n ⁢\n \n 𝑑\n x\n \n \n \n =\n \n \n ∫\n 0\n ∞\n \n \n \n {\n \n \n ∫\n \n \n ∂\n ⁡\n B\n \n ⁡\n \n (\n \n x\n 0\n \n ;\n r\n )\n \n \n \n \n \n f\n \n ⁢\n \n 𝑑\n S\n \n \n \n }\n \n ⁢\n \n 𝑑\n r\n \n \n \n \n \n \n \n \n \n subscript\n \n \n \n Q12916\n Q4440864\n \n \n \n \n Q853831\n \n differential-d\n Q50701\n \n \n \n \n \n \n \n subscript\n \n 0\n \n \n \n \n \n \n \n \n subscript\n \n \n \n \n Q838611\n \n \n subscript\n Q44946\n 0\n \n Q173817\n \n \n \n \n Q853831\n \n differential-d\n Q484298\n \n \n \n \n \n differential-d\n Q173817\n \n \n \n \n \n \\int_{\\mathbb{R}^{n}}f\\,dx=\\int_{0}^{\\infty}\\left\\{\\int_{\\partial B(x_{0};r)}f%\n\\,dS\\right\\}\\,dr\n \n", "uri": "https://en.formulasearchengine.com/w/index.php?oldid=22382#math22382.3", "title": "Coarea_formula", "type": "equation", "check": { "tree": false } }