data/90.json
{
"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",
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<csymbol cd=\"latexml\" id=\"p1.1.m1.1.20.cmml\" xref=\"p1.1.m1.1.20\">differential-d</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.21.cmml\" xref=\"p1.1.m1.1.21\">Q173817</csymbol>\n </apply>\n </apply>\n </apply>\n </apply>\n </annotation-xml>\n <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">\\int_{\\mathbb{R}^{n}}f\\,dx=\\int_{0}^{\\infty}\\left\\{\\int_{\\partial B(x_{0};r)}f%\n\\,dS\\right\\}\\,dr</annotation>\n </semantics>\n</math>",
"uri" : "https://en.formulasearchengine.com/w/index.php?oldid=22382#math22382.3",
"title" : "Coarea_formula",
"type" : "equation",
"check" : {
"tree" : false,
"qid" : null
}
}