A) \[\frac{1}{25}-\frac{6{{e}^{-5}}}{25}\]
B) \[\frac{1}{25}+\frac{6{{e}^{-5}}}{25}\]
C) \[-\frac{1}{25}-\frac{6{{e}^{-5}}}{25}\]
D) \[\frac{1}{25}-\frac{1}{5}{{e}^{-5}}\]
E) \[\frac{1}{25}+\frac{1}{5}{{e}^{-5}}\]
Correct Answer: A
Solution :
\[\int_{0}^{1}{\underset{I}{\mathop{x}}\,}\,\,\underset{II}{\mathop{{{e}^{-5x}}}}\,dx\] \[=\left[ \left\{ x\left( \frac{{{e}^{-5x}}}{-5} \right) \right\} \right]_{0}^{1}-\left\{ \int_{0}^{1}{1.\frac{{{e}^{-5x}}}{-5}dx} \right\}\] \[=\left[ -\frac{x{{e}^{-5x}}}{5}-\frac{{{e}^{-5x}}}{25} \right]_{0}^{1}\] \[=-\frac{{{e}^{-5}}}{5}-\frac{{{e}^{-5}}}{25}+\frac{1}{25}\] \[=-\frac{6{{e}^{-5}}}{25}+\frac{1}{25}=\frac{1}{25}-\frac{6{{e}^{-5}}}{25}\]
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