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Let d/(dx) (F(x))= e^(sinx)/x, x>0. If ...

Let `d/(dx) (F(x))= e^(sinx)/x, x>0`. If `int_1^4 (2e^sin(x^2))/x dx = F(k)-F(1)`, then possible value of k is:

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`I=int_(1)^(4)(2e^(sinx^(2)))/xdx=F(k)-F(1)=[F(x)]_(1)^(k)`
Now put `x^(2)=t`
`:.2xdx=dt`
`:.I=int_(1)^(16)(e^(sint))/tdt=[F(t)]_(1)^(16)`
`:.I=F(16)-F(1)`
`=:.k=16`
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