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KEAM 2019 Math Paper
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© examsnet.com
Question : 31
Total: 121
The area between the curve
y
=
2
x
4
−
x
2
, the
X
-axis and the ordinates of two minima of the curve is
5
120
11
120
13
120
7
120
9
120
Validate
Solution:
y
=
2
x
4
−
x
2
Differentiating w.r.t
x
.
d
y
d
x
=
8
x
3
−
2
x
For maxima or minima
d
y
d
x
=
0
x
=
−
1
2
,
0
,
1
2
d
2
y
d
x
2
=
24
x
2
−
2
(
d
2
y
d
x
)
a
t
x
=
−
1
2
>
0
,
(
d
2
y
d
x
2
)
x
=
0
<
0
,
(
d
2
y
d
x
2
)
x
=
1
2
>
0
∴
Required area
=
|
1
∕
2
∫
−
∕
1
∕
2
(
2
x
4
−
x
2
)
d
x
|
=
7
120
sq unit
© examsnet.com
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