find the area of the region bounded by the parabola x=4-y^2 and y axis
Answers
Answer
Given equations of curves are
x
2
=4y .......(1)
and, x=4y−2 ......(2)
Equation 1 represents a parabola which is open upward having vertex (0,0) and equation 2 represents a straight line.
On putting the value of 4y from equation 1 in equation 2, we get,
x=x
2
−2
x
2
−x−2=0
(x+1)(x−2)=0
x=−1,2
When x=−1, then from equation 1, y=
4
1
and when x=2, then from equation 1, y=1
Therefore, points of intersection of given curves are (−1,
4
1
) and (2,1).
Therefore,
Required area = Area of shaded region BOAB
=
−1
∫
2
[y(line)−y(parabola)]dx
=
−1
∫
2
[(
4
x+2
)−
4
x
2
]dx
=
4
1
−1
∫
2
(x+2−x
2
)dx
=
4
1
[(2+4−
3
8
)−(
2
1
−2+
3
1
)]
=
4
1
(6−
3
8
+2−
6
5
)
=
4
1
.
6
27
=
8
9
sq.units
Step-by-step explanation:
HOPE IT WILL HELP YOU DEAR FRIEND.....
PLZ FOLLOW ME......
AND MARK MY ANSWER IF YOU WISH.......
We need to find area bounded by the parabola,
and y axis, i.e.,
Assume,
Hence the area bounded will be given by,