Find volume of the solid generated by revolving

Question

Find volume of the solid generated by revolving the region bounded by the parabola $ =^2+1 ,=0 $ and the line =3 about the line =3

Using Disk method,I found the answer to be 9.4

Answer 1

$$V=\pi \int_{y_0}^{y_1} (R(y))^2dy$$ $$=\pi \int_{0}^{\sqrt{2}} (3-(y^2 +1))^2dy$$ $$=\frac{32\sqrt{2}\pi}{15}\approx 9.478$$

You're correct.

Answer 2

Consider interchange of axes for convenience:

$$ y =x^2 +1 $$

$$ \pi \int _{-\sqrt 2 }^ {+\sqrt 2} y^2 dx = \pi \int _{-\sqrt 2 }^ {+\sqrt 2} (x^2+1)^2 dx $$