Let $\frac{d}{{dx}}\;\,\,F\left( x \right) = \left( {\frac{{{e^{\sin x}}}}{x}} \right),\,\,x > 0$, If $\mathop \smallint \nolimits_1^4 \,\,\frac{3}{x}\,\,{e^{\sin {x^3}}}\;dx = F\left( k \right)\,\, - F\left( 1 \right)$, then one of the possible values of $k$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

Let

\frac{d}{{dx}}\;\,\,F\left( x \right) = \left( {\frac{{{e^{\sin x}}}}{x}} \right),\,\,x > 0

, If

\int \nolimits_1^4 \,\,\frac{3}{x}\,\,{e^{\sin {x^3}}}\;dx = F\left( k \right)\,\, - F\left( 1 \right)

, then one of the possible values of

k

, is

View answer and explanation

Correct option: D

\mathrm{64}

The correct answer is D (64) because after substitution and simplification, the value of k is found to be 64.

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