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Definite Integration question

2019 · 12 Jan · Shift 2 · Q24

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PYQ Library
JEE Main
Mathematics
Definite Integration
2019 · 12 Jan · Shift 2 · Q24

Definite Integration question

2019 · 12 Jan · Shift 2 · Q24

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The integral

\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,

loge x dx is equal to :

A
$- {1 \over 2} + {1 \over e} - {1 \over {2{e^2}}}$
B
${3 \over 2} - e - {1 \over {2{e^2}}}$
C
${1 \over 2} - e - {1 \over {{e^2}}}$
D
${3 \over 2} - {1 \over e} - {1 \over {2{x^2}}}$

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