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Question
Mathematics
Let f (x)=g (1) x2+x g prime x+g prime prime (x) and g (x) =x2+x f prime (1)+f prime prime (2) , then area bounded by y=g (x) and x-axis is
Q. Let
f
(
x
)
=
g
(
1
)
x
2
+
x
g
′
x
+
g
′′
(
x
)
and
g
(
x
)
=
x
2
+
x
f
′
(
1
)
+
f
′′
(
2
)
, then area bounded by
y
=
g
(
x
)
and
x
-axis is
36
117
NTA Abhyas
NTA Abhyas 2022
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A
9
B
2
9
C
2
27
D
27
Solution:
Clearly,
f
(
x
)
=
2
−
3
x
and
g
(
x
)
=
x
2
−
3
x
g
(
x
)
=
Area
=
∣
∣
0
∫
3
(
x
2
−
3
x
)
d
x
∣
∣
=
3
x
3
−
2
3
x
2
∣
0
3
=
∣
∣
9
−
2
27
∣
∣
=
∣
∣
2
−
9
∣
∣
=
2
9
.