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Find the area of the region enclosed by ...

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

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The correct Answer is:
N/a
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"`
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Knowledge Check

  • The area of the region bounded by the parabola y = x^(2) and the line y = 4x is

    A
    `32/3 sq. units`
    B
    `16/3 sq. units`
    C
    `8/3 sq. units`
    D
    `4/3 sq. units`

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