The area of common to the parabola y =
2x2 and y = x2 +4 is
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Answer:
Step-by-step explanation:
Find the P.O.I of the parabolas equate the equations y=2x
2
and y=x
2
+y we get
2x
2
=x
2
+4
x
2
=4
x=±2
y=8
∴ POI are A(−2,8) & C(2,8)
∴ the required are ABCD
A=∫
−2
2
(y
1
−y
2
)dx (where y
1
=x
2
+4&y
2
=2x
2
)
=∫
−2
2
(x
2
+4−2x
2
)dx=∫
−2
2
(4−x
2
)dx=(4x−
3
x
3
)
−2
2
[4(2)−
3
(2)
3
]−[4(−2)−
3
(−2)
3
]=[8−
3
8
]−[8+
3
8
]
=
3
32
sq. units
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