If $\phi '\,\,\left( x \right) = \frac{{{{\log }_e}\,\,\left| {\,\sin \,\,x\,} \right|}}{x},\;\,x \ne n\;\pi ,\,\;n \in Z$ and $\mathop \smallint \limits_1^3 \,\,\frac{{3\,\,{{\log }_e}\,\left| {\,\sin \,\,{x^3}\,} \right|}}{x}\,\,dx = \phi \,\,\left( 1 \right)$, then the possible value of $k$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\phi '\,\,\left( x \right) = \frac{{{{\log }_e}\,\,\left| {\,\sin \,\,x\,} \right|}}{x},\;\,x \ne n\;\pi ,\,\;n \in Z

and

\int \limits_1^3 \,\,\frac{{3\,\,{{\log }_e}\,\left| {\,\sin \,\,{x^3}\,} \right|}}{x}\,\,dx = \phi \,\,\left( 1 \right)

, then the possible value of

k

View answer and explanation

Correct option: A

\mathrm{27}

Option A (27) is correct because the integral is evaluated using substitution and the properties of definite integrals, resulting in k = 27.