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Mathematics
Mathematics
Problem
Let
d
d
x
(
F
(
x
)
)
=
e
sin
x
x
\frac{d}{dx}(F(x)) = \frac{e^{\sin x}}{x}
d
x
d
(
F
(
x
))
=
x
e
s
i
n
x
,
x
>
0
x > 0
x
>
0
. If
∫
1
4
2
e
sin
x
2
x
d
x
=
F
(
k
)
−
F
(
1
)
\int_{1}^{4} \frac{2e^{\sin x^2}}{x}\,dx = F(k) - F(1)
∫
1
4
x
2
e
s
i
n
x
2
d
x
=
F
(
k
)
−
F
(
1
)
, then one of the possible value of
k
k
k
is a. 4 b. 8 c. 16 d. 32
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