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Byju's Answer
Standard XII
Mathematics
Greatest Integer Function
Find the area...
Question
Find the area of the figure bounded by the following curves
y = sin x, y =
2
x
/
π
,
0
⩽
x
⩽
π
/
2.
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Solution
y
=
s
i
n
x
,
y
=
2
x
π
s
i
n
x
=
2
x
π
π
2
s
i
n
x
=
x
s
i
n
x
varies from
0
to
1
So,
x
=
0
or
x
=
π
2
π
2
Area under curve
=
∫
x
2
x
1
(
y
2
−
y
1
)
d
x
=
∫
π
2
0
(
s
i
n
x
−
2
x
π
)
d
x
=
−
c
o
s
x
−
x
2
π
]
π
2
0
=
−
c
o
s
π
2
−
π
2
4
π
+
c
o
s
0
+
0
π
=
1
−
π
4
Sq units
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0
Similar questions
Q.
Find the area of the figure bounded by the following curves
y =
(
x
−
1
)
2
,
+ y = 0, x = 2, x = 3.
Q.
Find the area of the figure bounded by the following curves
y = sin
x
2
,
y
=
2
x
/
π
,
Q.
Find the area of the figure bounded by the following curves
y
=
2
+
s
i
n
x
,
y
=
1.
+
c
o
s
2
x
,
x
=
0.
x
?
Q.
Assertion :The area bounded by the curve
y
=
sin
−
1
x
& the line x=0 &
|
y
|
=
π
2
is
√
2
square units. Reason: The domain & principal value branch of
y
=
sin
−
1
x
are [-1,1] &
[
−
π
2
,
π
2
]
respectively
Q.
Find the area bounded by the curve
y
=
sin
x
,
0
≤
x
≤
π
and line
y
=
1
√
2
.
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