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Find the area enclosed by the parabola y2 = 2x and the line x - y = 4.

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Given curves are

y2= 2x ........(i)

and the line x - y = 4......(ii)

Obviously, curve (i) is right handed parabola having vertex at (0, 0) and axis along +ve direction of x-axis while curve (ii) is a straight line.

For intersection point of curve (i) and (ii)

Intersection points are (2, - 2), (8, 4). Therefore. required area = Area of shaded region

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