find the area enclosed by a parabola y2=x and the line y +x=2 and the x axis
Answers
Answer:
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).
Step-by-step explanation:
Thus, required area =∫
−2
1
(2−y−y
2
)dy=[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.
Answer:
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
)dy=[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