Sketch & Find Volume of Rotated Shell: y=x^2+1, y=-1

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Homework Statement


I have to sketch a vertical or horizontal strip and state an expression for the volume of the shell formed by its rotation. Do not solve

y=x^2+1 x=0
y=1 x=1

around y=-1

Homework Equations





The Attempt at a Solution


I'm really lost because I don't know how to get started. I think dy works but I can't get it right. Any help will be great thanks.
 
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Have you figured out the shape in the plane? As a volume of revolution?
Pls post what you have for the integral so that we can see where you are stuck.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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