Combine the Sum of the Two Iterated Integrals into a Single

question 117

Multiple Choice

Combine the sum of the two iterated integrals into a single integral by converting to polar coordinates. Evaluate the resulting iterated integral. $$\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { x } \sqrt { x ^ { 2 } + y ^ { 2 } } d y d x + \int _ { 2 } ^ { 2 \sqrt { 2 } } \int _ { 0 } ^ { \sqrt { 8 - x ^ { 2 } } } \sqrt { x ^ { 2 } + y ^ { 2 } } d y d x$$

• A) \(\frac { 3 \sqrt { 2 } } { 8 \pi }\)
• B) \(\frac { 3 \pi } { 8 \sqrt { 2 } }\)
• C) \(\frac { 8 \pi } { 3 }\)
• D) \(\frac { 4 } { 3 } \sqrt { 2 } \pi\)
• E) \(\frac { 4 } { 3 } \pi\)

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