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Find the area enclosed by the figure des...

Find the area enclosed by the figure described by the equation `x^(4)+1=2x^(2)+y^(2).`

Text Solution

Verified by Experts

The correct Answer is:
`(8)/(3)` sq. units
`x^(4)+1=2x^(2)+y^(2)`
`therefore" "x^(4)-2x^(2)+1=y^(2)`
`therefore" "(x^(2)-1)^(2)=y^(2)`
`therefore" "y=pm(x^(2)-1),` which are two parabolas.

`"Required area "A=4overset(1)underset(0)int(1-x^(2))dx`
`=4[x-(x^(3))/(3)]_(0)^(1)=(8)/(3)` sq. units.
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