Question

If $\frac{d}{dx}f\left(x\right)=\frac{e^{sinx}}{x}$, x > 0 and ${\int }_1^4\frac{3e^{sin{x}^3}}{x}dx=f\left(k\right)-f\left(1\right)$ then one possible value of k is

• A. 64
• B. 32
• C. 16
• D. 8

Answer 1

The correct option is A 64

$f\left(x\right)=\int \frac{e^{sinx}}{x}dx$
$I={\int }_1^4\frac{3e^{sin{x}^3}}{x}dx={\int }_1^4\frac{3x^2{e}^{sin{x}^2}}{x^3}dx$
$=f\left(64\right)-f\left(1\right)$
$\Rightarrow k=64$