The graph of each function below is constructed from a quarter circle and two line segments. Using geometry, compute the following integrals.

\( \int _0^6 f(x) \d x =\int _0^2 f(x) \d x +\int _2^4 f(x) \d x +\int _4^6 f(x) \d x = \)

=Area(1/4 of a circle)+Area(triangle)+Area (square)

\[ \int _0^6 f(x) \d x = \answer {\pi +6} \]

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\[ \int _0^6 f(x) \d x = \answer {\pi -6} \]

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\[ \int _0^6 f(x) \d x = \answer {-\pi -6} \]

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\[ \int _0^6 f(x) \d x = \answer {-\pi +6} \]

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\[ \int _0^6 f(x) \d x = \answer {-\pi -2} \]

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\[ \int _0^6 f(x) \d x = \answer {2+\pi } \]