Find the area enclosed by the curve `y=-x^(2)` and the straight line `x+y+2=0`.

Answer

N/a

Explanation

We have, `y=-x^(2)" and "x+y+2=0`

`rArr -x-2=-x^(2)rArrx^(2)-x-2=0`
`rArr x^(2)+x-2x-2=0rArrx(x+1)-2(x+1)=0`
`rArr (x-2)(x+1)=0rArrx=2, -1`
`:. "Area of shaded region, " A=abs(int_(-1)^(2)(-x-2+x^(2))dx)=abs(int_(-1)^(2)(x^(2)-x-2)dx)`
`=abs([(x^(3))/3-(x^(2))/2-2x]_(-1)^(2))=abs([8/3-4/2-4+1/3+1/2-2])`
`=abs((16-12-24++3-12)/6)=abs(-27/6)=9/2" sq units"`