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Mathematics
Mathematics
Problem
Given,
f
(
x
)
=
sin
3
x
f(x) = \sin^3 x
f
(
x
)
=
sin
3
x
and
P
(
x
)
P(x)
P
(
x
)
is a quadratic polynomial with leading coefficient unity. Statement I
∫
0
2
π
P
(
x
)
⋅
f
′
′
(
x
)
d
x
\int_{0}^{2\pi} P(x) \cdot f''(x) dx
∫
0
2
π
P
(
x
)
⋅
f
′′
(
x
)
d
x
vanishes. Statement II
∫
0
2
π
f
(
x
)
d
x
\int_{0}^{2\pi} f(x) dx
∫
0
2
π
f
(
x
)
d
x
vanishes.
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