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Definite Integration question

2014 · Shift 2 · Q36

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2014 · Shift 2 · Q36

Definite Integration question

2014 · Shift 2 · Q36

JEE AdvancedMathematicsDefinite IntegrationMCQ+3 / −1

The following integral

\int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\left( {2\csc\,\,x} \right)}^{17}}dx}

is equal to

A
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} + {e^{ - u}}} \right)}^{16}}\,du}$
B
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {{{\left( {{e^u} + {e^{ - u}}} \right)}^{17}}\,du}$
C
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {{{\left( {{e^u} - {e^{ - u}}} \right)}^{17}}\,du}$
D
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} - {e^{ - u}}} \right)}^{16}}\,du}$

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