Find the area of the region bounded by the curve y = 2x - x? and x-axis
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Answer:
Given y=2x−x
2
, x−axis
the points x-axis cuts the curves are
0=2x−x
2
=x(2−x)
x=0 or x=2
so the points are
A=(0,0) , B=(2,0)
Required area=∫
0
2
2x−x
2
dx
=[x
2
−
3
x
3
]
0
2
=2
2
−
3
2
3
−0=4−
3
8
=
3
4
∴ Area=
3
4
sq units
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