Set Up (But Do Not Evaluate)an Iterated Integral to Compute $z = x ^ { 2 } + y ^ { 2 }$

question 63

Multiple Choice

Set up (but do not evaluate) an iterated integral to compute the mass of the solid paraboloid bounded by $z = x ^ { 2 } + y ^ { 2 }$ and z = 1, if the density is given by $\delta$ (x, y, z) = z².

• A) \(\text { Mass } = \int _ { - 1 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 1 } z ^ { 2 } d z d x d y\)
• B) \(\text { Mass } = \int _ { 0 } ^ { 1 } \int _ { 0 } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 1 } z ^ { 2 } d z d y d x\)
• C) \(\operatorname { Mass } = \int _ { - 1 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { 0 } ^ { 1 } z ^ { 2 } d z d y d x\)
• D) \(\text { Mass } = \int _ { - 1 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 1 } z ^ { 2 } d z d y d x\)
• E) \(\text { Mass } = \int _ { 0 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { 1 } z ^ { 2 } d z d y d x\)

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