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KEAM 2019 Math Paper
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© examsnet.com
Question : 59
Total: 121
If
I
=
1.5
∫
0
[
x
2
]
d
x
, then
I
is equal to
2
+
√
2
√
2
−
1
2
0
2
−
√
2
Validate
Solution:
Let
x
2
=
t
d
x
=
1
2
√
t
d
t
I
=
2
⋅
25
∫
0
[
t
]
2
√
t
d
t
=
1
∫
0
[
t
]
2
√
t
d
t
+
2
∫
1
[
t
]
2
√
t
d
t
+
225
∫
2
[
t
]
2
√
t
d
t
=
0
+
2
∫
1
1
2
√
t
d
t
+
225
∫
2
2
2
√
t
d
t
=
[
√
t
]
1
2
+
[
2
√
t
]
2
225
=
(
√
2
−
1
)
+
2
(
1.5
−
√
2
)
=
2
−
√
2
© examsnet.com
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