What is the area bounded by the curves `|y| = 1-x^(2)` ?

Options

A. `4/3` square units
B. `8/3` square units
C. `4` square units
D. `16/3` square units

Answer

B

Explanation

Since `|y|= {{:(y,ygt0),(-y,ylt0),(0,y=0):}`
For `y gt 0 rArr y = 1-x^(2)`
For `y lt 0rArr y = x^(2)- 1`
For `y = 0 rArr x = +-1`
So area under the curve
`= 4 xx "Area under the regoin OABO (symmetry)"`
`= 4 xxint_(0)^(1) 1-x^(2) dx `
`= 4 xx [x- (x^(3))/(3)]_(0)^(1)]`
`= 4(1-1/3) = 4 xx 2/3 = 8/3` sq. units`
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