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Byju's Answer
Standard XII
Mathematics
Integration of Piecewise Continuous Functions
The value of ...
Question
The value of
[
∫
π
4
0
2
(
1
+
x
)
ln
(
1
+
x
)
⋅
sin
x
+
cos
x
2
(
1
+
x
)
cos
3
x
d
x
]
is (where [.] denotes the greatest integer function)
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Solution
I
=
∫
π
4
0
(
2
ln
(
1
+
x
)
sin
x
cos
x
+
cos
2
x
1
+
x
2
cos
4
x
)
d
x
∫
π
4
0
1
2
d
(
ln
(
1
+
x
)
cos
2
x
)
=
1
2
[
ln
(
1
+
x
)
cos
2
x
]
π
4
0
=
ln
(
1
+
π
4
)
So, [
I
] = 0
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1
Similar questions
Q.
The value of
[
∫
π
4
0
2
(
1
+
x
)
ln
(
1
+
x
)
⋅
sin
x
+
cos
x
2
(
1
+
x
)
cos
3
x
d
x
]
is (where [.] denotes the greatest integer function)
Q.
The value of
lim
x
→
π
/
2
⎡
⎢ ⎢
⎣
x
−
π
2
cos
x
⎤
⎥ ⎥
⎦
(where , [x] denotes greatest integer function) is
Q.
f
(
x
)
=
1
+
[
cos
x
]
, in
0
<
x
≤
π
2
(where
[
.
]
denotes greatest integer function)
Q.
f
(
x
)
=
1
+
[
cos
x
]
x
in
0
<
x
≤
π
/
2
, where
[
]
denotes greatest integer function then-
Q.
Discuss the continuity of the function
[
cos
x
]
at
x
=
π
2
, where
[
.
]
denotes the greatest integer function.
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