Let $\frac{d}{d x}(F(x))=\frac{e^{\sin x}}{x}, x > 0$ If $\int_\limits 1^4 \frac{2 e^{\sin x^2}}{x} d x=F(k)-F(1)$, 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}{d x}(F(x))=\frac{e^{\sin x}}{x}, x > 0

\int\limits_{1}^4 \frac{2 e^{\sin x^2}}{x} d x=F(k)-F(1)

, then one of the possible values of

k

, is

View answer and explanation

Correct option: C

Option C is correct. By using substitution and the given derivative, the integral simplifies to F(16) - F(1), thus k=16.

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