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Byju's Answer
Standard XII
Mathematics
Orthocenter
The area boun...
Question
The area bounded by the curve y = f (x), x-axis, and the ordinates x = 1 and x = b is
(b −1) sin (3b + 4). Then, f (x) is
(a) (x − 1) cos (3x + 4)
(b) sin (3x + 4)
(c) sin (3x + 4) + 3 (x − 1) cos (3x +4)
(d) none of these
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Solution
(c) sin (3x + 4) + 3 (x − 1) cos (3x +4)
y
=
f
x
If
A
is
the
the
area
bound
by
the
curve
,
x
-
axis
,
x
=
1
and
x
=
b
⇒
∫
1
b
f
x
d
x
=
A
1
b
=
b
-
1
sin
3
b
+
4
Given
⇒
f
x
=
d
d
x
x
-
1
sin
3
x
+
4
=
sin
3
x
+
4
d
d
x
x
-
1
+
x
-
1
d
d
x
sin
3
x
+
4
=
sin
3
x
+
4
+
3
x
-
1
cos
3
x
+
4
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0
Similar questions
Q.
The area bounded by the curve y=f(x), x-axis and ordinates x = 1 and x=b is
(
b
−
1
)
s
i
n
(
3
b
+
4
)
, then f(x) is
Q.
The area bounded by the curve y = f (x), x-axis, and the ordinates x = 1 and x = b is
(b −1) sin (3b + 4). Then, f (x) is
(a) (x − 1) cos (3x + 4)
(b) sin (3x + 4)
(c) sin (3x + 4) + 3 (x − 1) cos (3x +4)
(d) none of these
Q.
The area bounded by the curve
y
=
f
(
x
)
, x-axis and the ordinates
x
=
1
and
x
=
b
is
(
b
−
1
)
sin
(
3
b
+
4
)
, then
f
(
x
)
equals-
Q.
If
f
(
x
)
is given by
f
(
x
)
=
(
cos
x
+
i
sin
x
)
(
cos
3
x
+
i
sin
3
x
)
.
.
.
.
(
cos
(
2
n
−
1
)
x
+
i
sin
(
2
n
−
1
)
x
)
, then
f
′′
(
x
)
is equal to
Q.
The area bounded by the curve
y
=
f
(
x
)
, the
x
−
axis and the ordinates
x
=
1
and
x
=
b
is
(
b
−
1
)
cos
(
3
b
+
4
)
sq.unit. Then
f
(
x
)
is given by:
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