Find the area bounded by the parabola x² =8y and y²=8x
Answers
Answer:y
2
=8x and x
2
=8y
the points of intersection
x
2
/8=
8x
8
2
x
3
=8
x=0 and x=8
So, area b//w curves is
0
∫
8
(
8x
−x
2
/8)dx
8
0
∫
8
x
dx−
0
∫
8
(
8
x
3
)dx=
3
2
8
(x)
3/2
∣
0
8
−1/8
3
x
3
∣
0
8
2/38
2
−1/8(8
3
/3)
=
3
2.8
2
−8
2
/3=
3
64
squnitsy
2
=8x and x
2
=8y
the points of intersection
x
2
/8=
8x
8
2
x
3
=8
x=0 and x=8
So, area b//w curves is
0
∫
8
(
8x
−x
2
/8)dx
8
0
∫
8
x
dx−
0
∫
8
(
8
x
3
)dx=
3
2
8
(x)
3/2
∣
0
8
−1/8
3
x
3
∣
0
8
2/38
2
−1/8(8
3
/3)
=
3
2.8
2
−8
2
/3=
3
64
squnitsy
2
=8x and x
2
=8y
the points of intersection
x
2
/8=
8x
8
2
x
3
=8
x=0 and x=8
So, area b//w curves is
0
∫
8
(
8x
−x
2
/8)dx
8
0
∫
8
x
dx−
0
∫
8
(
8
x
3
)dx=
3
2
8
(x)
3/2
∣
0
8
−1/8
3
x
3
∣
0
8
2/38
2
−1/8(8
3
/3)
=
3
2.8
2
−8
2
/3=
3
64
squnits