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Câu hỏi: Tích phân $\int\limits_{1}^{3}{\left( 4{{x}^{3}}+1 \right)\text{d}x}$ bằng:
A. $80$.
B. $322$.
C. $82$.
D. $22$.
A. $80$.
B. $322$.
C. $82$.
D. $22$.
Ta có:
$\int\limits_{1}^{3}{\left( 4{{x}^{3}}+1 \right)\text{d}x}=\left( {{x}^{4}}+x \right)\left| \begin{aligned}
& 3 \\
& 1 \\
\end{aligned} \right.=\left( {{3}^{4}}+3 \right)-\left( {{1}^{4}}+1 \right)=82$.
$\int\limits_{1}^{3}{\left( 4{{x}^{3}}+1 \right)\text{d}x}=\left( {{x}^{4}}+x \right)\left| \begin{aligned}
& 3 \\
& 1 \\
\end{aligned} \right.=\left( {{3}^{4}}+3 \right)-\left( {{1}^{4}}+1 \right)=82$.
Đáp án C.