Discussion
Between zero and two, the polynomial \( 3x^{2} + 2x \) integrates to
Answer: C
Integrate term by term and substitute the limits:
\[ \int_{0}^{2}\left(3x^{2} + 2x\right)dx \;=\; \left[x^{3} + x^{2}\right]_{0}^{2} \;=\; 8 + 4 \;=\; 12. \]
The two pieces contribute eight and four respectively, so taking either alone accounts for the eight offered as a distractor
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