A) 15
B) 16
C) 63
D) 64
Correct Answer: D
Solution :
\[\frac{d}{dx}F(x)=\frac{{{e}^{\sin x}}}{x}\]\[\Rightarrow \int_{\,1}^{\,4}{\frac{3}{x}{{e}^{\sin {{x}^{3}}}}dx=\int_{\,1}^{\,4}{\frac{3{{x}^{2}}}{{{x}^{3}}}{{e}^{\sin {{x}^{3}}}}dx}}\] Put \[{{x}^{3}}=t\,\,\,\Rightarrow 3\,{{x}^{2}}dx=dt\] \[F(t)=\int_{1}^{64}{\frac{{{e}^{\sin t}}}{t}\,}dt=\int_{1}^{64}{F(t)dt=F(64)-F(1)},\] On comparing, \[k=64.\]You need to login to perform this action.
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