Math, asked by candycrush19, 1 month ago

Find the volume of solid generated by revolving the region between parabola x=y^2+1 and the line x=3 about the line x=3

Answers

Answered by Barani22
0

Answer:

.

Step-by-step explanation:

expressed as,

Volume=π∫

b

a

(f1(x)−f2(x))dy

Consider,

x =f1(x)=3 x =f2(x)=y2+1

Comapring the expression of x,

3 =y2+1 y2 =3−1 y =±

2

y =−

2

,

2

Substituting the values of limits and f1(x),f2(x) in the expression of the volume,

Volume =π∫

2

2

(3−(y2+1))dy =π∫

2

2

(2−y2)dy =π[2y−

y3

3

]

2

2

Applying the limits over the integral,

Volume =π[2

2

(

2

)3

3

+2

2

(−

2

)3

3

] =π[4

2

(

2

)3

3

+

(

2

)3

3

] =4

2

π

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