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Mathematics
Mathematics
Problem
The value of
∫
0
x
[
t
+
1
]
3
d
t
\int_{0}^{x} [t + 1]^3 dt
∫
0
x
[
t
+
1
]
3
d
t
(where,
[
.
]
[.]
[
.
]
denotes the greatest integer function of
x
x
x
) is equal to a.
(
[
x
]
(
[
x
]
+
1
)
2
)
2
+
(
[
x
]
+
1
)
3
{
x
}
\left( \frac{[x]([x]+1)}{2} \right)^2 + ([x]+1)^3 \{x\}
(
2
[
x
]
([
x
]
+
1
)
)
2
+
([
x
]
+
1
)
3
{
x
}
b.
(
[
x
]
(
[
x
]
+
1
)
2
)
3
+
(
[
x
]
+
1
)
3
{
x
}
\left( \frac{[x]([x]+1)}{2} \right)^3 + ([x]+1)^3 \{x\}
(
2
[
x
]
([
x
]
+
1
)
)
3
+
([
x
]
+
1
)
3
{
x
}
c.
(
[
x
]
(
[
x
]
+
1
)
2
)
3
+
(
[
x
]
+
1
)
2
{
x
}
\left( \frac{[x]([x]+1)}{2} \right)^3 + ([x]+1)^2 \{x\}
(
2
[
x
]
([
x
]
+
1
)
)
3
+
([
x
]
+
1
)
2
{
x
}
d. None of these
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