Find the volume of the solid obtained by revolving tge loop of the curve a^2 y^2 = x^2 (2a-x)(x-a) about x axis
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Step-by-step explanation:
We have to find the volume of the solid 2ay
2
=x(x−a)
2
Put y=0
⇒x=0,x=a
Therefore Required volume =π∫
0
a
2a
x(x−a)
2
dx
=
2a
π
∫
0
a
x(x
2
−2ax+a
2
)dx
=
2a
π
∫
0
a
(x
3
−2ax
2
+a
2
x)dx
=
2a
π
[
4
x
4
−
3
2ax
3
+
2
a
2
x
2
]
0
a
=
2a
πa
4
[
12
3−8+6
]
=
24
πa
3
Hence the required volume is
24
πa
3
cu.units
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