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Câu hỏi: Tích phân $\int\limits_{1}^{2}{{{e}^{2x}}dx}$ bằng
A. $\dfrac{{{e}^{2}}}{2}$.
B. ${{e}^{4}}-{{e}^{2}}$.
C. $2\left( {{e}^{4}}-{{e}^{2}} \right)$.
D. $\dfrac{{{e}^{4}}-{{e}^{2}}}{2}$.
A. $\dfrac{{{e}^{2}}}{2}$.
B. ${{e}^{4}}-{{e}^{2}}$.
C. $2\left( {{e}^{4}}-{{e}^{2}} \right)$.
D. $\dfrac{{{e}^{4}}-{{e}^{2}}}{2}$.
Ta có: $\int\limits_{1}^{2}{{{e}^{2x}}dx}=\dfrac{1}{2}\int\limits_{1}^{2}{{{e}^{2x}}d\left( 2x \right)}=\left. \dfrac{1}{2}{{e}^{2x}} \right|_{1}^{2}=\dfrac{{{e}^{4}}-{{e}^{2}}}{2}$.
Đáp án D.