Set Up but Do Not Evaluate a (Multiple)integral That Gives $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 2$

question 44

Multiple Choice

Set up but do not evaluate a (multiple) integral that gives the volume of the solid bounded above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 2$ and below by the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ .

• A) \(\int _ { - 1 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { \sqrt { 2 - x ^ { 2 } - y ^ { 2 } } } d x d y d z\)
• B) \(\int _ { - 1 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { - x ^ { 2 } - y ^ { 2 } } ^ { \sqrt { 2 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• C) \[
• \int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}} \int_{x^{2}+y^{2}}^{\sqrt{2-x^{2}-y^{2}}}\]\( d z d y d x \)
• D) \(\int _ { - 1 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { \sqrt { 2 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• E) \(\int _ { 0 } ^ { 1 } \int _ { - \sqrt { 1 - x ^ { 2 } } } ^ { \sqrt { 1 - x ^ { 2 } } } \int _ { x ^ { 2 } + y ^ { 2 } } ^ { \sqrt { 2 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)

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