Let $${d \over {dx}}\,F\left( x \right) = {{{e^{\sin x}}} \over x},\,x > 0.$$ If $$\int_1^4 {{{2{e^{\sin {x^2}}}} \over x}} \,\,dx = F\left( k \right) - F\left( 1 \right)$$
then one of the possible values of $$k$$ is ............
Answer
$$16$$
2
IIT-JEE 1997
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The value of $$\int_1^{{e^{37}}} {{{\pi \sin \left( {\pi In\,x} \right)} \over x}\,dx} $$ is ...............