Find the area of the region enclosed by the parabola `x^(2)=y` and the line y = x+ 2.

Answer

N/a

Explanation

We have,` x^(2)=y" and "y=x+2`
`rArrx^(2)=c+2`
`rArrx^(2)-x-2=0`
`rArrx^(2)-2x+x-2=0`
`rArrx(x-2)+1(x-2)=0`
`rArr(x+1)(x-2)=0`
`rArrx=-1, 2`

`:. "Required area of shaded region "=int_(-1)^(2)(x+2-x^(2))dx=[(x^(2))/2+2x-(x^(3))/3]_(-1)^(2)`
`=[4/2+4-8/3-1/2+2-1/3]`
`=6+3/2-9/3=(36+9-18)/6=27/6=9/2" sq units"`