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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: $\int\limits_{1}^{2}{{{e}^{2x}}dx=\dfrac{1}{2}\int\limits_{1}^{2}{{{e}^{2x}}d\left( 2x \right)=\left. \dfrac{1}{2}{{e}^{2x}} \right|}}_{1}^{2}=\dfrac{1}{2}\left( {{e}^{4}}-{{e}^{2}} \right).$
Đáp án D.