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JEE Main Math Class 12 Application of Integrals Questions
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© examsnet.com
Question : 5
Total: 78
Let
a
and
b
respectively be the points of local maximum and local minimum of the function
f
(
x
)
=
2
x
3
−
3
x
2
−
12
x
. If A is the total area of the region bounded by
y
=
f
(
x
)
, the X- axis and the lines
x
=
a
and
x
=
b
, then
4
A
is equal to
[26 Aug 2021 Shift 2]
Your Answer:
Validate
Solution:
We have,
f
(
x
)
=
2
x
3
−
3
x
2
−
12
x
∴
f
′
(
x
)
=
6
x
2
−
6
x
−
12
=
6
(
x
2
−
x
−
2
)
=
6
(
x
+
1
)
(
x
−
2
)
f'(x) = 0
⇒
x
=
−
1
and 2
∴
x
=
−
1
and 2 are critical points
∴
a
=
−
1
and
b
=
2
Now, required area,
A
0
=
0
∫
−
1
f
(
x
)
d
x
+
2
∫
0
−
f
(
x
)
d
x
0
∫
−
1
(
2
x
3
−
3
x
2
−
12
x
)
d
x
+
2
∫
0
(
12
x
+
3
x
2
−
2
x
3
)
d
x
=
[
x
4
2
−
x
3
−
6
x
2
]
−
1
0
+
[
6
x
2
+
x
3
−
x
4
2
]
0
2
=
114
4
∴
4
A
=
114
© examsnet.com
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