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प्रश्न
Find the area of the region bounded by the parabola y2 = x and the line y = x – 2
उत्तर
First find the intersecting point of y2 = x and y = x – 2
y = y2 – 2
y2 – y – 2 = 0
y = 2, y = – 1
Intersecting points are (4, 2),(1, – 1)
Area required = `int_"c"^"d" (x_"R" - x_"L") "d"y`
= `int_(- 1)^2 (y + 2) "d"y - int_(- 1)^2 y^2 "d"y`
= `[y^2/2 + 2y]_(-1)^2 - [y^3/3]_(- 1)^2`
= `[2 + 4 - 1/2 + 2] - [8/3 + 1/3]`
= `15/2 - 3`
= `9/2`
Required Area = `9/2` sq.units
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