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If is a polynomial function such that and and
MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals
Problem
If
f
(
x
)
f(x)
f
(
x
)
is a polynomial function such that
f
(
x
)
+
f
′
(
x
)
+
f
′
′
(
x
)
+
f
′
′
′
(
x
)
=
x
3
f(x) + f'(x) + f''(x) + f'''(x) = x^3
f
(
x
)
+
f
′
(
x
)
+
f
′′
(
x
)
+
f
′′′
(
x
)
=
x
3
and
g
(
x
)
=
∫
f
(
x
)
x
3
d
x
g(x) = \int \frac{f(x)}{x^3}\,dx
g
(
x
)
=
∫
x
3
f
(
x
)
d
x
and
g
(
1
)
=
1
g(1) = 1
g
(
1
)
=
1
, then
⌈
g
(
e
)
⌉
\lceil g(e) \rceil
⌈
g
(
e
)⌉
is (where
⌈
⋅
⌉
\lceil \cdot \rceil
⌈
⋅
⌉
denotes greatest integer function and
e
e
e
is Napier's constant)
Related theory
Differentiation Rules
Antiderivatives
Standard algebraic integrals
Integration as inverse process of differentiation
Integrals
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