Question

find the area enclosed by a parabola y2=x and the line y +x=2 and the x axis

Answer 1

Answer:

Solution

Verified by Toppr

To get the point of intersection, we have to solve the equation of line

Y+

x=

2

and parabola

y 2

x

.

On solving them we find the coordinates of points of intersection as (4,−2) and (1,1). Drawing perpendiculars from these points on y-axis, we obtain the coordinate as (0,1) and (0,−2).

Thus, required area

=

∫

−2

1

(2−

y−

y 2

[2y−

2

y 2

−

3

y 3

] 1−

−2

= (2−

2

1

−

3

1

)− (

4

−

−

2

4

+

8

3

)

= 2−

6

5

+ 6−

3

8

= 8−

6

21

=

6

27

=

2

9

sq.units