Question

The area of the region enclosed by the parabola x² = y, the line y = x + 2 and the x-axis, is 

पर्याय

• `2/9`

• `9/2`

• 9

• 2

Answer 1

`9/2`

Explanation:

y = x² is a parabola with vertex (0, 0) and axis of parabola is y-axis.

For intersection of y = x² and y = x + 2

x² = x + 2

⇒ x² – x – 2 = 0

⇒ (x – 2)(x + 1) = 0

⇒ x = – 1, 2

For y = x + 2

`{:(x, -1, 0),(y, 1, 2):}`

= `int_(-1)^2 (x + 2)  dx - int_(-1)^2  x^2  dx = [(x + 2)^2/2]_(-1)^2 + [- x^3/3]_(-1)^2`

= `9/2` sq.units