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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a differentiable function such that its derivative
f
′
f'
f
′
is continuous and
f
(
π
)
=
−
6
f(\pi) = -6
f
(
π
)
=
−
6
. If
F
:
[
0
,
π
]
→
R
F: [0, \pi] \to \mathbb{R}
F
:
[
0
,
π
]
→
R
is defined by
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
F(x) = \int_{0}^{x} f(t) dt
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
, and if
∫
0
π
(
f
′
(
x
)
+
F
(
x
)
)
cos
x
d
x
=
2
\int_{0}^{\pi} (f'(x) + F(x)) \cos x \, dx = 2
∫
0
π
(
f
′
(
x
)
+
F
(
x
))
cos
x
d
x
=
2
, then the value of
f
(
0
)
f(0)
f
(
0
)
is _____ [JEE-Advanced 2020]
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