Question

Find the area of the region included between the parabola y2 = x and the line x + y = 2?



































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Answer 1

• x + y=2 --------(1)

• y2=x ----------(2)

• Equation (1) represents a straight line which meets the co-ordinates axis at (0,2) and (2,0) respectively.

• Equation 2 Represents a parabola with vertex at the origin and axis along +ve x axis.

• The point of intersection of parabola and line are given as  

Substituting x from eq. (2) in eq. (1)

y2 + y -2 = 0

(y+2)(y-1)=0

y=1,-2

putting the values of y in eq. (1)

at y=1,        x=1

at y=-2,      x=4

• The area enclosed by the line and parabola can be refer below-