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Find the area of the figure bounded by t...

Find the area of the figure bounded by the parabolas `x=-2y^2, x=1-3y^2dot`

Text Solution

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`x = -2y^(2)`
`x = -3y^(2) + 1`
On solving , we get
`implies y^(2) - 1 = 0`
`implies y = pm`
`therefore` Area = `int_(-1)^(1) [(1-3y^(2)) - (-2y^(2))]`dy
`int_(-1)^(1) (1-y^(2))`dy
`= [y - (y^(3))/(3)]_(1)^(1)`
`= (2)/(3) - ((-2)/(3))`
`= (4)/(3)` sq. units
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