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
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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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