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(Solved): Use cylindrical coordinates to calculate : \\[ \\begin{array}{l} \\iiint_{\\mathcal{W}} x^{2}+y^{2} ...




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Use cylindrical coordinates to calculate : \\[ \\begin{array}{l} \\iiint_{\\mathcal{W}} x^{2}+y^{2} d V \\quad \\mathcal{W}: x^{2}+y^{2} \\leq 16, \\quad 0 \\leq z \\leq 14 \\\\ \\iiint_{\\mathcal{W}}\\left(x^{2}+y^{2}\\right) d V= \\end{array} \\]


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Use the cylindrical coordinates we put   
Therefore   

Trigonometric identity we have   


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