Question

find the volume of solid obtained by revolving the loop of the curve a^2y^2=x^2(2a-x) (x-a) about x axis

Answer 1

Answer:

We have to find the volume of the solid 2ay

2

=x(x−a)

2

The graph of the curve is shown below

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

Step-by-step explanation:

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