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Byju's Answer
Standard XII
Mathematics
Area between x=g(y) and y Axis
Let fx be a...
Question
Let
f
x
be a continuous function such that the area bounded by the curve
y
=
f
(
x
)
, the
x
-axis and the two ordinates
x
=
0
and
x
=
a
is
a
2
2
+
a
2
sin
a
+
π
2
cos
a
.Then
f
(
π
2
)
is
Open in App
Solution
a
∫
0
f
(
x
)
=
a
2
2
+
a
2
2
sin
a
+
π
2
cos
a
By Leibniz rule
→
d
=
g
(
x
)
∫
h
(
x
)
(
x
)
d
x
d
.
d
d
x
=
f
(
g
(
x
)
)
g
′
(
x
)
−
f
h
(
x
)
)
h
′
(
x
)
∴
f
(
a
)
−
0
=
a
+
a
2
2
cos
a
+
a
sin
A
−
π
2
sin
a
∴
f
(
a
)
=
a
+
(
a
−
π
2
)
sin
A
+
a
2
2
cos
a
∴
f
(
x
)
=
x
+
x
2
2
cos
x
+
(
x
−
π
2
)
sin
x
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Similar questions
Q.
Let
f
(
x
)
be a continuous function such that the area bounded by the curve
y
=
f
(
x
)
, the
x
−
axis and the two ordinates
x
=
0
and
x
=
a
is
(
a
2
2
+
a
2
sin
a
+
π
2
cos
a
)
.sq.unit, then
f
(
π
2
)
is
Q.
Let
f
(
x
)
be a continuous function such that the area bounded by the curve
y
=
f
(
x
)
, x-axis and the lines
x
=
0
and
x
=
a
is
a
2
2
+
a
2
sin
a
+
π
2
cos
a
, then
f
(
π
2
)
=
Q.
Let
f
(
x
)
be a non-negative continuous function such that the area bounded by the curve
y
=
f
(
x
)
, x-axis and the ordinates
x
=
π
4
,
x
=
β
>
π
4
is
(
β
sin
β
+
π
4
cos
β
+
√
2
β
−
π
2
)
. Then
f
(
π
2
)
is
Q.
If
f
(
x
)
be a continuous function such that the area bounded by the curve
y
=
f
(
x
)
, the
x
-axis, and the lines
x
=
0
and
x
=
a
is
1
+
a
2
2
sin
a
, then
Q.
Let
f
(
x
)
be a non-negative continuous and differentiable function such that the area bounded by the curve
y
=
f
(
x
)
x axis and the ordinate
x
=
π
4
and
x
=
β
>
π
4
is
(
β
sin
β
+
π
4
cos
β
+
√
2
β
)
then
f
1
(
0
)
is
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