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Mathematics
Mathematics
Problem
The value of
∫
1
2
(
x
⌊
x
2
⌋
+
⌊
x
2
⌋
x
)
d
x
\int_{1}^{2} (x^{\lfloor x^2 \rfloor} + \lfloor x^2 \rfloor^x) \, dx
∫
1
2
(
x
⌊
x
2
⌋
+
⌊
x
2
⌋
x
)
d
x
is equal to where
[
⋅
]
[\cdot]
[
⋅
]
denotes the greatest integer function a.
5
4
+
3
+
(
2
3
−
2
2
)
+
1
log
3
(
9
−
3
3
)
\frac{5}{4} + \sqrt{3} + (2\sqrt{3} - 2\sqrt{2}) + \frac{1}{\log 3} (9 - 3\sqrt{3})
4
5
+
3
+
(
2
3
−
2
2
)
+
l
o
g
3
1
(
9
−
3
3
)
b.
5
4
+
3
+
2
3
+
1
log
2
(
2
3
−
2
2
)
+
1
log
3
(
9
−
3
3
)
\frac{5}{4} + \sqrt{3} + \frac{\sqrt{2}}{3} + \frac{1}{\log 2} (2\sqrt{3} - 2\sqrt{2}) + \frac{1}{\log 3} (9 - 3\sqrt{3})
4
5
+
3
+
3
2
+
l
o
g
2
1
(
2
3
−
2
2
)
+
l
o
g
3
1
(
9
−
3
3
)
c.
5
4
+
2
3
+
1
log
2
(
2
3
−
2
2
)
+
1
log
3
(
9
−
3
3
)
\frac{5}{4} + \frac{\sqrt{2}}{3} + \frac{1}{\log 2} (2\sqrt{3} - 2\sqrt{2}) + \frac{1}{\log 3} (9 - 3\sqrt{3})
4
5
+
3
2
+
l
o
g
2
1
(
2
3
−
2
2
)
+
l
o
g
3
1
(
9
−
3
3
)
d. None of the above
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